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In this work, the Hirota bilinear symbolic computational method along with test functions and the generalized exponential rational function method are capitalized to secure soliton and lump solutions to the Sharma–Tasso–Olver–Burgers equation. Several novel soliton solutions are observed in unique patterns such as periodic, exponential, hyperbolic, dark, singular, and combo forms. Additionally, we also extract interaction, lump and breather solutions of the governing model. The novel characteristic of this work is the attained results, which were not before computed. Modulation instability of the governing equation is also examined via linear stability theory. To demonstrate the physical aspects and configuration of the attained solitons, some distinct graphs are plotted in different shapes. The validity of the solutions is verified by using Mathematica. The constructed outcomes are very encouraging and entail that the concerned methods can be utilized to acquire assorted improved, innovative, and advantageous outcomes for miscellaneous remarkable nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

Understanding the intricate Korteweg–de Vries ( c K d V ) equation is paramount for comprehending various nonlinear wave phenomena, owing to its capacity to depict the propagation of nonlinear waves in media characterized by complex-valued dispersive and nonlinear coefficients. The practical ramifications of the c K d V equation are extensive, spanning disciplines such as optics, plasma physics, and other realms dealing with intricate media. This investigation employs the Khater II method and a generalized rational approach as analytical methodologies to generate novel exact solutions for the c K d V equation. The Khater II method is employed to transform the nonlinear partial differential equation into a nonlinear ordinary differential equation, thus facilitating a systematic resolution. Moreover, the generalized rational technique utilizes a rational ansatz function to derive diverse forms of solutions. Application of these methodologies leads to the discovery of fresh exact solutions, encompassing solitary and periodic wave solutions for the c K d V equation. These solutions are expressed in rational forms featuring arbitrary functions, thereby expanding the repertoire of known solutions for the model. The efficacy of the analytical methodologies employed becomes evident through the discovery of these novel exact solutions, thereby enriching our understanding of the physical interpretations and wave characteristics associated with the c K d V equation. The derived solutions augment the existing body of knowledge pertaining to the model. This research enhances our comprehension of the c K d V equation, thereby advancing nonlinear wave analysis with potential applications in physics, optics, plasma science, and allied engineering domains. Future investigations may explore the extension of these methodologies to address other nonlinear wave equations. [ABSTRACT FROM AUTHOR]

The Rastall–Rainbow gravity theory has recently been proposed as a combination of the Rastall and rainbow theories. This theory can be thought as a generalization of the Rastall gravity to an energy dependent Rastall theory, and leads to an additional degrees of freedom. In this paper, we construct models that admit the wormhole geometries within this theory. We analyze the properties of static wormholes based on the profiles of dark matter halos, which was demonstrated earlier in Rahaman et al. (Eur Phys J C 74:2750, 2014) that galactic halo possesses the necessary properties in favour of the existence of wormholes. The main properties are being analyzed by considering three different kinds of halo density profiles. Our results indicate that such wormholes could potentially exist but the NEC is violated in the vicinity of the wormhole throat. We have further examined the stability of the configuration through the adiabatic sound velocity. [ABSTRACT FROM AUTHOR]

The present work looks for the possible existence of static and spherically symmetric wormhole geometries in Rastall–Rainbow gravity. Since, the Rastall–Rainbow gravity model has been constructed with the combination of Rastall theory and the gravity's rainbow formalism. Taking advantage of the Karmarkar condition for embedding class one metrics, we solve the modified field equations analytically that describe wormholes for specific choice of redshift function. For specific parameter ranges, the solution represents a traversable wormhole that exhibits the violation of null energy condition and consequently the weak energy condition also. Furthermore, we focus on the wormhole stability via adiabatic sound velocity analysis. This model establishes a strong connection between two model parameters, namely, the Rastall parameters and the Rainbow functions, and how it affects the wormhole solution. [ABSTRACT FROM AUTHOR]

This study delves into investigating the stability of solutions pertaining to the generalized Davey–Stewartson ( D S ) equation by employing the generalized rational method and projective Riccati equations method within the Hamiltonian system framework. The central focus lies in unraveling the physical significance of this model within the realm of plasma physics, shedding light on its intricate connections with analogous equations. The generalized D S equation, a pivotal nonlinear evolution model, serves as a vital tool in comprehending the evolution of coupled waves across various physical systems, notably within the domains of fluid dynamics and plasma physics. Its significance lies in its capacity to elucidate the intricate interplay among different wave components, offering a holistic perspective on wave interactions within plasma mediums. Through the meticulous application of rigorous analytical methods, this investigation uncovers pivotal insights into the stability of solutions, thereby enriching our understanding of mathematical models in plasma physics. The findings presented in this research contribute significantly to advancing the understanding of nonlinear dynamics, with profound implications for future exploration in plasma physics and related fields. In essence, this study underscores the analytical prowess of the generalized rational and projective Riccati equations methods, accentuating their relevance and applicability to the generalized D S equation and, by extension, their role in enhancing our comprehension of coupled wave phenomena within diverse plasma systems. [ABSTRACT FROM AUTHOR]

This paper mainly concentrates on obtaining solutions and other exact traveling wave solutions using the generalized G-expansion method. Some new exact solutions of the coupled nonlinear Schrödinger system using the mentioned method are extracted. This method is based on the general properties of the nonlinear model of expansion method with the support of the complete discrimination system for polynomial method and computer algebraic system (AS) such as Maple or Mathematica. The nonparaxial solitons with the propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide is studied. To attain this, an illustrative case of the coupled nonlinear Helmholtz (CNLH) system is given to illustrate the possibility and unwavering quality of the strategy utilized in this research. These solutions can be significant in the use of understanding the behavior of wave guides when studying Kerr medium, optical computing and optical beams in Kerr like nonlinear media. Physical meanings of solutions are simulated by various Figures in 2D and 3D along with density graphs. The constraint conditions of the existence of solutions are also reported in detail. Finally, the modulation instability analysis of the CNLH equation is presented in detail. [ABSTRACT FROM AUTHOR]

This manuscript introduces a novel bidirectional wave dynamics to the q-deformed Sinh-Gordon model. The main objective of this study is to investigate the simultaneous motion of two symmetrical waves. The ϕ 6 -model expansion technique is used for achieving the required objective. The ϕ 6 -model expansion technique extracts new solitary wave solutions for the proposed model. Moreover, we delve into the mathematical aspects and explore the physical characteristics of the q-deformed Sinh-Gordon equation in its bidirectional form. The study provides intricate derivations of the innovative solutions, accompanied by visual representations that offer insights into their physical structures. The findings of this investigation significantly contribute to our comprehension of this model. Finally, fascinating three-dimensional plots and two-dimensional line plots are displayed. [ABSTRACT FROM AUTHOR]

The cultivation of grapes encounters various challenges, such as the presence of pests and diseases, which have the potential to considerably diminish agricultural productivity. Plant diseases pose a significant impediment, resulting in diminished agricultural productivity and economic setbacks, thereby affecting the quality of crop yields. Hence, the precise and timely identification of plant diseases holds significant importance. This study employs a Convolutional neural network (CNN) with and without data augmentation, in addition to a DCNN Classifier model based on VGG16, to classify grape leaf diseases. A publicly available dataset is utilized for the purpose of investigating diseases affecting grape leaves. The DCNN Classifier Model successfully utilizes the strengths of the VGG16 model and modifies it by incorporating supplementary layers to enhance its performance and ability to generalize. Systematic evaluation of metrics, such as accuracy and F1-score, is performed. With training and test accuracy rates of 99.18 and 99.06%, respectively, the DCNN Classifier model does a better job than the CNN models used in this investigation. The findings demonstrate that the DCNN Classifier model, utilizing the VGG16 architecture and incorporating three supplementary CNN layers, exhibits superior performance. Also, the fact that the DCNN Classifier model works well as a decision support system for farmers is shown by the fact that it can quickly and accurately identify grape diseases, making it easier to take steps to stop them. The results of this study provide support for the reliability of the DCNN classifier model and its potential utility in the field of agriculture. [ABSTRACT FROM AUTHOR]

This research focuses on the design of a novel fractional model for simulating the ongoing spread of the coronavirus (COVID-19). The model is composed of multiple categories named susceptible S (t) , infected I (t) , treated T (t) , and recovered R (t) with the susceptible category further divided into two subcategories S 1 (t) and S 2 (t) . In light of the need for restrictive measures such as mandatory masks and social distancing to control the virus, the study of the dynamics and spread of the virus is an important topic. In addition, we investigate the positivity of the solution and its boundedness to ensure positive results. Furthermore, equilibrium points for the system are determined, and a stability analysis is conducted. Additionally, this study employs the analytical technique of the Laplace Adomian decomposition method (LADM) to simulate the different compartments of the model, taking into account various scenarios. The Laplace transform is used to convert the nonlinear resulting equations into an equivalent linear form, and the Adomian polynomials are utilized to treat the nonlinear terms. Solving this set of equations yields the solution for the state variables. To further assess the dynamics of the model, numerical simulations are conducted and compared with the results from LADM. Additionally, a comparison with real data from Italy is demonstrated, which shows a perfect agreement between the obtained data using the numerical and Laplace Adomian techniques. The graphical simulation is employed to investigate the effect of fractional-order terms, and an analysis of parameters is done to observe how quickly stabilization can be achieved with or without confinement rules. It is demonstrated that if no confinement rules are applied, it will take longer for stabilization after more people have been affected; however, if strict measures and a low contact rate are implemented, stabilization can be reached sooner. [ABSTRACT FROM AUTHOR]

Marine structure changes as a result of climate change, with potential biological implications for human societies and marine ecosystems. These changes include changes in temperatures, flow, discrimination, nutritional inputs, oxygen availability, and acidification of the ocean. In this study, a fractional-order model is constructed using the Caputo fractional operator, which singular and nol-local kernel. A model examines the effects of accelerating global warming on aquatic ecosystems while taking into account variables that change over time, such as the environment and organisms. The positively invariant area also demonstrates positive, bounded solutions of the model treated. The equilibrium states for the occurrence and extinction of fish populations are derived for a feasible solution of the system. We also used fixed-point theorems to analyze the existence and uniqueness of the model. The generalized Ulam-Hyers-Rassias function is used to analyze the stability of the system. To study the impact of the fractional operator through computational simulations, results are generated employing a two-step Lagrange polynomial in the generalized version for the power law kernel and also compared the results with an exponential law and Mittag Leffler kernel. We also produce graphs of the model at various fractional derivative orders to illustrate the important influence that the fractional order has on the different classes of the model with the memory effects of the fractional operator. To help with the oversight of fisheries, this research builds mathematical connections between the natural world and aquatic ecosystems. [ABSTRACT FROM AUTHOR]

In this paper the K-Nearest Neighbor (KNN) model which is one of machine learning (ML) algorithm is applied to distinguish between the four distinct Hermite Gaussian (HG) beams (HG00, HG01, HG02, and HG03) in mode division multiplexed (MDM)-free space optics (FSO) communication system. First, the performance of the FSO system using these different HG beams is investigated for rainy weather conditions in various Indian cities having distinct geographical locations. Transmission performance is evaluated in terms of quality (Q)-factor, signal-to-noise ratio (SNR), bit error rate (BER), and eye diagrams. Then, the values of the BER for the different HG beams are applied to the KNN ML model as to classify between them. HG modes are used for capacity enhancement. Results indicate that 80 Gbps can be transmitted over 1000 m in Hyderabad, 800 m in Pune, 580 m in Chennai, and 475 m in Mumbai at log (BER) ~ 10 - 15 , Q-factor less than 8, and SNR ~ 10 dB. Additionally, the K-Nearest Neighbor (KNN) ML model shows 94% classification accuracy between four HG beams. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an anisotropic model using a dark matter (DM) density profile in Einstein–Gauss–Bonnet (EGB) gravity using a gravitational decoupling method introduced by Ovalle (Phys Rev D 95:104019, 2017), which has provided an innovative approach for obtaining solutions to the EGB field equations for the spherically symmetric structure of stellar bodies. The Tolman and Finch–Skea (TFS) solutions of two metric potentials, g tt and g rr , have been used to construct the seed solution. Additionally, the presence of DM in DM halos distorts spacetime, causing perturbations in the g rr metric potential, where the quantity of DM is determined by the decoupling parameter β . The physical validity of the solution, along with stability and equilibrium analysis, has also been performed. Along with stability and equilibrium analysis, the solution’s physical validity has also been examined. Additionally, we have shown how both constants affect the physical characteristics of the solution. Using a M - R diagram, it has been described how the DM component and the GB constant affect the maximum permissible masses and their corresponding radii for various compact objects. Our model predicts the masses beyond the 2 M ⊙ and maximum radii 11. 92 - 0.01 + 0.02 and 12. 83 - 0.02 + 0.01 for larger value of α under density order 10 15 g / cm 3 and 10 14 g / cm 3 , respectively, while the radii become 11. 96 - 0.01 + 0.01 and 12. 81 - 0.02 + 0.01 for larger value of β . [ABSTRACT FROM AUTHOR]

We introduce a notion of nonlinear cyclic orbital (ξ − F) -contraction and prove related results. With these results, we address the existence and uniqueness results with periodic/anti-periodic boundary conditions for: 1. The nonlinear multi-order fractional differential equation L (D) θ (ς) = σ (ς , θ (ς)) , ς ∈ J = [ 0 , A ] , A > 0 , where L (D) = γ w c D δ w + γ w − 1 c D δ w − 1 + ⋯ + γ 1 c D δ 1 + γ 0 c D δ 0 , γ ♭ ∈ R (♭ = 0 , 1 , 2 , 3 , ... , w) , γ w ≠ 0 , 0 ≤ δ 0 < δ 1 < δ 2 < ⋯ < δ w − 1 < δ w < 1 ; 2. The nonlinear multi-term fractional delay differential equation L (D) θ (ς) = σ (ς , θ (ς) , θ (ς − τ)) , ς ∈ J = [ 0 , A ] , A > 0 ; θ (ς) = σ ¯ (ς) , ς ∈ [ − τ , 0 ] , where L (D) = γ w c D δ w + γ w − 1 c D δ w − 1 + ⋯ + γ 1 c D δ 1 + γ 0 c D δ 0 , γ ♭ ∈ R (♭ = 0 , 1 , 2 , 3 , ... , w) , γ w ≠ 0 , 0 ≤ δ 0 < δ 1 < δ 2 < ⋯ < δ w − 1 < δ w < 1 ; moreover, here D δ c is predominantly called Caputo fractional derivative of order δ. [ABSTRACT FROM AUTHOR]

In this article, we discuss the exact controllability of a fractional order differential system involving Hilfer fractional(HF) derivative, state-dependent delay function and impulsive conditions. To obtain the proposed result, we use the semigroup theory, theory of measure of non-compactness and fixed point technique. Finally, an example is given to illustrate the application of the obtained results. [ABSTRACT FROM AUTHOR]

In this investigation, we unfold the Jensen–Mercer ( J − M ) inequality for convex stochastic processes via a new fractional integral operator. The incorporation of convex stochastic processes, the J − M inequality and a fractional integral operator having an exponential kernel brings a new direction to the theory of inequalities. With this in mind, estimations of Hermite–Hadamard–Mercer ( H − H − M )-type fractional inequalities involving convex stochastic processes are presented. In the context of the new fractional integral operator, we also investigate a novel identity for differentiable mappings. Then, a new related H − H − M -type inequality is presented using this identity as an auxiliary result. Applications to special means and matrices are also presented. These findings are particularly appealing from the perspective of optimization, as they provide a larger context to analyze optimization and mathematical programming problems. [ABSTRACT FROM AUTHOR]

This article is primarily targeting the approximate controllability of nonlocal Atangana–Baleanu fractional derivative by Mittag-Leffler kernel to stochastic differential systems. In particular, we obtain a new set of sufficient conditions for the approximate controllability of nonlinear Atangana–Baleanu fractional stochastic differential inclusions under the assumption that the corresponding linear system is approximately controllable. In addition, we establish the approximate controllability results for the Atangana–Baleanu fractional stochastic control system with infinite delay. The results are obtained with the help of the fixed-point theorem for multivalued operators and fractional calculus. At last, an example is included to show the applicability of our results. [ABSTRACT FROM AUTHOR]

The present works focus on the effects of electric and magnetic fields on the flow of micro-polar nano-fluid between two parallel plates with rotation under the impact of Hall current (EMMN-PPRH) has considered by using Artificial Neural Networks with the scheme of Levenberg–Marquardt backpropagation (ANN-SLMB). The nonlinear PDEs are transformed into nonlinear ODEs by employing similarity variables. By varying different parameters such as coupling parameter, electric parameter, rotation parameter, viscosity parameter, Prandtl number and the Brownian motion parameter, a dataset for recommended ANN-SLMB is produced for numerous scenarios through utilizing homotopy analysis method (HAM). The ANN-SLMB training, testing and validation technique have been used to analyze the approximate solution of individual cases, and the recommended model has matched for confirmation. After that, regression analysis, MSE, and histogram investigations were utilized to validate the proposed ANN-SLMB. The recommended technique is distinguished nearest of the suggested and reference findings, with an accuracy level ranging from 10−09 to 10−11. [ABSTRACT FROM AUTHOR]

This paper investigates the issue of existence and approximate controllability results for impulsive fractional differential inclusions with delay of order r ∈ (1 , 2 ] in Banach space. To begin, we analyze existence results for impulsive fractional evolution inclusions with delay using fractional calculations, the r-order cosine family, multivalued maps, and Martelli’s fixed point theorem. The approximate controllability results for impulsive fractional evolution inclusions with delay were then derived using Gronwall’s inequality and the sequence method. Then, we investigate the Sobolev fractional integrodifferential inclusions with finite delay. Moreover, we develop the nonlocal conditions in a given system. Finally, an example is presented to illustrate the main results. [ABSTRACT FROM AUTHOR]

There are some contributions analyzing the censored medical datasets using modifications of the conventional lifetime distribution; however most of the said contributions did not considered the modification of the Weibull distribution (WD). The WD is an important lifetime model. Due to its prime importance in modeling life data, many researchers have proposed different modifications of WD. One of the most recent modifications of WD is Modified Weibull Extension distribution (MWED). However, the ability of MWED to model the censored medical data has not yet been explored in the literature. We have explored the suitability of the model in modeling censored medical datasets. The analysis has been carried out using Bayesian methods under different loss functions and informative priors. The approximate Bayes estimates have been computed using Lindley's approximation. Based on detailed simulation study and real life analysis, it has been concluded that Bayesian methods performed better as compared to maximum likelihood estimates. In case of small samples, the performance of Bayes estimates under ELF and informative prior was the best. However, in case of large samples, the choice of prior and loss function did not affect the efficiency of the results to a large extend. The MWED performed efficiently in modeling real censored datasets relating to survival times of the leukemia and bile duct cancer patients. The MWED was explored to be a very promising candidate model for modeling censored medical datasets. [ABSTRACT FROM AUTHOR]

In present research manuscript, analysis is presented for the influences of heat transition in a bodewadt flow over a penetrable disk numerically. Estimation parameters in current mathematical flow model include magnetic field parameter (0.1 ≤ M ≤ 1.2) , wall suction (1.7 ≤ A ≤ 6.7) , prandtl number (0.2 ≤ Pr ≤ 5.0) , heat generation/absorption (- 0.9 ≤ Q ≤ 3.6) , eckert number (0 ≤ E c ≤ 1.2) , variable viscosity (- 100 ≤ θ e ≤ 100) and thermal conductivity (0 ≤ ε ≤ 4.1). The repercussions of joule heating, wall suction, heat generation & absorption, magnetic field, viscous dissipation accompanying with variable characteristics of the fluid are also examined as well. Kinetics of viscous fluid with variable characteristics of fluid having solid body rotation over a permeable disk (having cylindrical geometry) are analyzed. We transformed the governing equations of heat transfer (accompanied by variable properties) and fluid motion in to self-similar non-dimensional differential equations by using the Von-Karman variables which are then further analyzed numerically by utilizing Adams Bashforth method. For a physical insight, results are manifested to scrutinize the behavior of velocity and temperature profiles for different emerging parameters graphically. Moreover, the values of nusselt number & skin friction co-efficient are also computed and physically explicated for the assorted parameters. Outcomes of current investigations are compared with prior work, to ensure the authenticity of the numerical method, and strong agreement is noted. [ABSTRACT FROM AUTHOR]

The coupled fractional Fourier transform F α , β is a two-dimensional fractional Fourier transform depending on two angles α and β, which are coupled in such a way that the transform parameters are γ = (α + β) / 2 and δ = (α − β) / 2 . It generalizes the two-dimensional Fourier transform and serves as a prominent tool in some applications of signal and image processing. In this article, we formulate a new class of uncertainty inequalities for the coupled fractional Fourier transform (CFrFT). Firstly, we establish a sharp Heisenberg-type uncertainty inequality for the CFrFT and then formulate some logarithmic and local-type uncertainty inequalities. In the sequel, we establish several concentration-based uncertainty inequalities, including Nazarov, Amrein–Berthier–Benedicks, and Donoho–Stark's inequalities. Towards the end, we formulate Hardy's and Beurling's inequalities for the CFrFT. [ABSTRACT FROM AUTHOR]

In the present paper, fluid flow and heat transfer for micropolar fluids over a stretching sheet through Darcy porous medium are studied. The heat transfer phenomenon is considered with the isothermal wall as well as the isoflux boundary conditions. The fluid flow and heat transfer phenomena are modeled in the form of coupled nonlinear partial differential equations. The numerical solution is obtained using a nonstandard finite difference approximation on a quasi-uniform mesh. The numerical results obtained by the present approach are compared to those obtained by the Runge–Kutta fourth order method to demonstrate the accuracy of the present method. The numerical results obtained by both methods show excellent agreement. The effect of various physical parameters, namely the Reynolds number, Prandtl number, micropolar material parameters, injection/suction parameter, heat index parameter on bulk fluid speed, temperature distribution, and spin behavior of microstructures are demonstrated and discussed graphically. The simplicity of the finite difference approximation makes the selected technique more significant in the numerical study of micropolar fluid. The boundary layer thickness reduces with the increasing value of injection/suction parameter, Reynolds number, and micropolar parameter. The thermal boundary layer also reduces with the increment in the value of the micropolar parameter, Prandtl number, heat index parameter while microrotation increases with the increasing value of the injection/suction parameter. [ABSTRACT FROM AUTHOR]

The present study investigates the micropolar Jeffrey fluid flow in the presence of magnetic field across a stretching surface through porous medium. Through suitable similarity transformations, the governing partial differential equations are transformed into nonlinear ordinary differential equations and been solved numerically using MATLAB software (built-in solver called bvp4c boundary value problem fourth order collocation method) which establish the numerical solutions for such transformed nonlinear ordinary differential equations. The numerical solution for fluid velocity, micro-rotation and temperature thus obtained are explained graphically in which the influence of various pertinent parameters like magnetic parameter, porosity parameter, spin gradient viscosity parameter, unsteadiness parameter, Jeffrey fluid parameter, etc., on velocity, micro-rotation and temperature profiles has been studied and discussed. The plotted results are discussed for flow and heat transfer characteristics. [ABSTRACT FROM AUTHOR]

This study investigates the hotness transport and entropy creation of a time-dependent Prandtl–Eyring half and half nanofluid (P-EHNF). The flow and heat transport features of P-EHNF are analysed by subjecting the nanofluid to the slippage heated surface. The effects of the shapes of the nanosolid molecule, porosity material, Cattaneo–Christov heat flux, and radiative transition are likewise associated with this assessment. In a system of partial differential equalities (PDEs), the transcendent stream conditions are planned. Keller box mathematical strategy is a technique used to recognise the self-similar answer for recipes changed into ordinary differential equalities (ODEs) utilising legitimate changes. Two types of nanoparticles, copper (Cu) and graphene oxide (GO) with engine oil (EO) as the base liquid are considered in this review. Significant outcomes for the various factors are drawn up graphically in the streaming, energy, surface friction, Nusselt sum and entropic estimation. The imperative consequence of this investigation is that the heat transmission pace of P-EHNF (GO–Cu/EO) is more than the customary nanofluid (Cu–EO). Likewise, heat transport is the highest for circular-shaped and the lowest for lamina-shaped nanostrong particles. With the upgrade of nanoparticles size ϕ , the entropy is supported in the model. A similar impact likewise occurs with progress in radiative stream N r and Prandtl–Eyring variable α ∗ . [ABSTRACT FROM AUTHOR]

This document is a correction notice for an article titled "Analytical investigations of propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide by three computational ideas" published in Scientific Reports. The correction addresses an error in the affiliation of one of the authors. The correct affiliation is listed as the Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj, Saudi Arabia. The original article has been corrected. The authors of the article are Yuanyuan Liu, Jalil Manafian, Gurpreet Singh, Naief Alabed Alkader, and Kottakkaran Sooppy Nisar. [Extracted from the article]

This article discussed the influence of activation energy on MHD flow of third-grade nanofluid model (MHD-TGNFM) along with the convective conditions and used the technique of backpropagation in artificial neural network using Levenberg–Marquardt technique (BANN-LMT). The PDEs representing (MHD-TGNFM) transformed into the system of ODEs. The dataset for BANN-LMT is computed for the six scenarios by using the Adam numerical method by varying the local Hartman number (Ha), Prandtl number (Pr), local chemical reaction parameter (σ), Schmidt number (Sc), concentration Biot number (γ2) and thermal Biot number (γ1). By testing, validation and training process of (BANN-LMT), the estimated solutions are interpreted for (MHD-TGNFM). The validation of the performance of (BANN-LMT) is done through the MSE, error histogram and regression analysis. The concentration profile increases when there is an increase in Biot number and the local Hartmann number; meanwhile, it decreases for the higher values of Schmidt number and the local chemical reaction parameter. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying the approximate controllability for second-order impulsive differential inclusions with infinite delay. For proving the main results, we use the results related to the cosine and sine function of operators, Martelli's fixed point theorem, and the results when combined with the properties of differential inclusions. Firstly, we prove the approximate controllability for second-order impulsive differential inclusions with initial conditions. Then, we extend the discussion to the second-order impulsive system with nonlocal conditions. Finally, we provide an example for the illustration of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

The current flow model is dedicated to capture the role of Dufour and Soret on heat and mass transmission of rotating flow of γ Al 2 O 3 - C 2 H 6 O 2 and γ Al 2 O 3 - water nanoparticles due to exponential stretching under the action of thermal radiation, magnetic, and Eckert numbers. The problem is modelled in terms if partial differential equations (PDEs) with associated physical conditions. The ordinary differential equations (ODEs) are obtained via suitable transformations. The reduced nonlinear ODEs set is tackled via a new scheme. We suggested significant improvements in the traditional technique and further formulated an extended version of wavelets scheme-based Chebyshev polynomials thoughts. The detailed procedure of the wavelet scheme and flow chart are provided. To validate the numerical outcomes; a comparative study with numerical technique RK (order-4) is also provided. Furthermore; numerical consequences of velocity, concentration and temperature profiles are further examined using several plots. The graphical plots, compared and convergence analyses are endorsing that our proposed modifications are worthy. Velocities profiles in view of γ Al 2 O 3 - C 2 H 6 O 2 nanofluid are lower than the γ Al 2 O 3 - H 2 O nanofluid. Temperature and concentration profiles are dominant when γ Al 2 O 3 - H 2 O nanofluid is considered. [ABSTRACT FROM AUTHOR]

In the given research, our main goal is to explore new soliton solutions in (2 + 1) -dimensional Heisenberg ferromagnetic spin chain (HFSC) equation. This was achieved via the extended (G ′ / G 2) -expansion method. For this, we first analyse the given (2 + 1) -dimensional HFSC system of a partial differential equation (PDE) that is obtained by separating the equation into real and imaginary parts. The solution of our equation is determined as rapidly convergent sequences effectively computed by using Mathematica software. Furthermore, a special class of nonlinear wave solutions like periodic, straight, decreasing, dark-singular soliton and dark bright singular soliton were obtained in Heisenberg ferromagnetic dynamics. The amplitude of the soliton is determined by giving different values of parameters. With a suitable choice of parameters, 3D and 2D graphical illustrations are reported. The methodology applied is effective for obtaining exact solutions for various fractional partial differential equations in complex medium. The numerical module of the results obtained is studied, with fascinating figures showing the physical significance of the solutions. [ABSTRACT FROM AUTHOR]

The current communication is designed by keeping in the mind high heat transfer capabilities of nanoliquids with the dispersion of diversified-natured nanoparticles in poorly conducting base liquids. Here, an amalgamation of metallic (Cu) and hybridization of metallic and non-metallic oxide (Cu-TiO2) nanoparticles to uplift thermophysical attributes of water is deliberated. The magnetically affected flow between rotating disks under the impact and permeability aspect is assumed. Empirical relations for effective dynamic viscosity, density, and heat capacitance to show mesmerizing features of obliged nanoparticles are also expressed. In addition, mathematical relations also depend on morphological factors like shape, size, and diameter of inducted nanoparticles. The mathematical formulation of the problem is conceded in the form of a system of ODEs after using similarity transformation on dimensional PDEs. Simulations of the complex coupled differential structure are solved by using a numerical approach by employing shooting and Runge–Kutta procedures jointly. The impact of flow concerning variables on associated distributions is revealed through tabular and graphical manner. Quantities of engineering interest associated with work like wall friction and thermal flux coefficients at walls of the disk are also calculated. It is deduced from an examination that the addition of metallic particles raises heat transfer more than non-metallic particles. A significant impression of magnetic field on shear stress is executed by hybrid nanoparticles along the surface of disks. In addition, elevation in Nusselt number and depreciation in skin friction coefficient is revealed against increasing magnitude of nanoparticle volume fraction. A positive trend in skin friction coefficient is manifested against the increasing magnitude of Reynold number. It is also observed that by increasing the size and shape of hybrid nanoparticles thermal conductivity and viscosity of the base fluid increases. [ABSTRACT FROM AUTHOR]

The magnetohydrodynamics (MHD) viscous Jeffrey heat transport flow past a permeable extending sheet is analyzed. The Alumina ( A l 2 O 3 ) is chosen as nanoparticles immersed in sodium alginate ( SA ) as the based fluid. The effect of heat generation, Ohmic heating and viscous dissipation are also being investigated adopting Tiwari and Das model. The adequate similarity transformation is used to convert the governing equations to non-linear of higher-order ordinary differential equations (ODEs). The numerical solution of the transformed ODEs is accomplished using a finite-difference technique. The results are described in graphs according to selected parameters' values provided. The flow velocity reductions when the porosity parameter is augmented. The thermal distribution is affected by the presence of Pr , M , β , γ ∗ , δ ∗ and ϕ . Deborah number and the volume fraction of nanoparticles affect the skin friction coefficient in opposite ways. A higher volume percentage of nanoparticles and a higher Deborah number are both shown to boost the rate of heat transfer. These findings suggest that the concentration of nanoparticles can be used to manipulate heat transport and nanofluid motions. [ABSTRACT FROM AUTHOR]

This study aim to examine the channel flow of a couple stress Casson fluid. The flow is generated due to the motion of the plate at y = 0 , while the plate at y = d is at rest. This physical phenomenon is derived in terms of partial differential equations. The subjected governing PDE's are non-dimensionalized with the help of dimensionless variables. The dimensionless classical model is generalized by transforming it to the time fractional model using Fick's and Fourier's Laws. The general fractional model is solved by applying the Laplace and Fourier integral transformation. Furthermore, the parametric influence of various physical parameters like Casson parameter, couple stress parameter, Grashof number, Schmidt number and Prandtl number on velocity, temperature, and concentration distributions is shown graphically and discussed. The heat transfer rate, skin friction, and Sherwood number are calculated and presented in tabular form. It is worth noting that the increasing values of the couple stress parameter λ deaccelerate the velocity of Couple stress Casson fluid. [ABSTRACT FROM AUTHOR]

MHD Natural convection, which is one of the principal types of convective heat transfer in numerous research of heat exchangers and geothermal energy systems, as well as nanofluids and hybrid nanofluids. This work focuses on the investigation of Natural convective heat transfer evaluation inside a porous triangular cavity filled with silver-magnesium oxide/water hybrid nanofluid [H2O/Ag-MgO]hnf under a consistent magnetic field. The laminar and incompressible nanofluid flow is taken to account while Darcy–Forchheimer model takes account of the advection inertia effect in the porous sheet. Controlled equations of the work have been approached nondimensional and resolved by Galerkin finite element technique. The numerical analyses were carried out by varying the Darcy, Hartmann, and Rayleigh numbers, porosity, and characteristics of solid volume fraction and flow fields. Further, the findings are reported in streamlines, isotherms and Nusselt numbers. For this work, the parametric impact may be categorized into two groups. One of them has an effect on the structural factors such as triangular form and scale on the physical characteristics of the important outputs such as fluidity and thermal transfer rates. The significant findings are the parameters like Rayleigh and slightly supported by Hartmann along with Darcy number, minimally assists by solid-particle size and rotating factor as clockwise assists the cooler flow at the center and anticlockwise direction assists the warmer flow. Clear raise in heat transporting rate can be obtained for increasing solid-particle size. [ABSTRACT FROM AUTHOR]

The importance of nanoparticle shape on the flow of nanofluid for the application of energy conversion, micromixing, etc., is vital. The study reveals the flow of a conducting nanofluid to enrich the heat transfer phenomena considering F e 3 O 4 - water-based nanofluid. The flow past a radically extended sheet for the influence of radiative heat energy. As a novelty, the study takes place considering various shapes of the proposed nanoparticles such as column, sphere, hexahedron, tetrahedron, and lamina. A suitable similar transformation is imposed for the governing equations to convert into a set of ODEs. Further, a numerical technique with help of in-build code bvp5c is used for the solution of the transformed problem. However, the physical behavior of several parameters on the flow phenomena as well as engineering coefficients is displayed via graphs and elaborated. [ABSTRACT FROM AUTHOR]

In current study, analysis is presented for peristaltic motion of applied magnetic field and entropy generation within couple stress (Cu/H2O) nanofluid through an endoscope. An endoscope contains two coaxial cylindrical tubes in which the internal tube is nonflexible while the external tube has sinusoidal wave passing through the boundary. Influences of mixed convection along with applied magnetic field are encountered as well. Formulated governing model is fabricated introducing long wavelength and creeping Stokesian flow approximation which are then analyzed numerically by utilizing Adams Bashforth method. For a physical insight, results are demonstrated to examine the behaviors of flow profiles and entropy generation number for emerging flow parameters with the help of graphs, bar-charts and tables. [ABSTRACT FROM AUTHOR]

Solar thermal systems have low efficiency due to the working fluid's weak thermophysical characteristics. Thermo-physical characteristics of base fluid depend on particle concentration, diameter, and shapes. To assess a nanofluid's thermal performance in a solar collector, it is important to first understand the thermophysical changes that occur when nanoparticles are introduced to the base fluid. The aim of this study is, therefore, to analyze the hydrodynamic and heat characteristics of two different water-based hybrid nanofluids (used as a solar energy absorber) with varied particle shapes in a porous medium. As the heat transfer surface is exposed to the surrounding environment, the convective boundary condition is employed. Additionally, the flow of nanoliquid between two plates (in parallel) is observed influenced by velocity slip, non-uniform heat source-sink, linear thermal radiation. To make two targeted hybrid nanofluids, graphene is added as a cylindrical particle to water to make a nanofluid, and then silver is added as a platelet particle to the graphene/water nanofluid. For the second hybrid nanofluid, CuO spherical shape particles are introduced to the graphene/water nanofluid. The entropy of the system is also assessed. The Tiwari-Das nanofluid model is used. The translated mathematical formulations are then solved numerically. The physical and graphical behavior of significant parameters is studied. [ABSTRACT FROM AUTHOR]

The nanofluid flows play a vital role in many engineering processes owing to their notable industrial usage and excessive heat transfer abilities. Lately, an advanced form of nanofluids namely "hybrid nanofluids" has swapped the usual nanofluid flows to further augment the heat transfer capabilities. The objective of this envisaged model is to compare the performance of two renowned hybrid nanofluid models namely Hamilton–Crosser and Yamada–Ota. The hybrid nanoliquid (TiO2-SiC/DO) flow model is comprised of Titanium oxide (TiO2) and Silicon carbide (SiC) nanoparticles submerged into Diathermic oil (DO). The subject flow is considered over a stretched surface and is influenced by the magnetic dipole. The uniqueness of the fluid model is augmented by considering the modified Fourier law instead of the traditional Fourier law and slip conditions at the boundary. By applying the suitable similarity transformations, the system of ordinary differential equations obtained from the leading partial differential equations is handled by the MATLAB solver bvp4c package to determine the numerical solution. It is divulged that the Yamada–Ota model performs considerably better than the Hamilton–Crosser flow model as far as heat transfer capabilities are concerned. Further, the velocity reduces on increasing hydrodynamic interaction and slip parameters. It is also noted that both temperature profiles increase for higher hydrodynamic interaction and viscous dissipation parameters. The envisioned model is authenticated when compared with an already published result in a limiting case. [ABSTRACT FROM AUTHOR]

In this paper, the authors derive some new generalizations of fractional trapezium-like inequalities using the class of harmonic convex functions. Moreover, three new fractional integral identities are given, and on using them as auxiliary results some interesting integral inequalities are found. Finally, in order to show the efficiency of our main results, some applications to special means for different positive real numbers and error estimations for quadrature formulas are obtained. [ABSTRACT FROM AUTHOR]

In this paper, the perturbed Gerdjikov–Ivanov (GI) equation using a truncated M-fractional derivative is studied in mathematical nonlinear optics. We are explored its novel dark and other soliton solutions and compared them with the existing results. To obtain the objective, two particular methods, the modified extended tanh expansion method and the E x p a function method, are implemented. In this exercise, an arrangement of exact solitons is received as well as verified by utilizing the symbolic soft computations. The dynamical characteristics of the obtained results, along with a fractional parameter, are also discussed via two and three-dimensional graphs. These solutions are suggested that the employed methods are impressive, determined and smooth as compared to many other methods. The work of this paper is of high importance regarding its applications in photonic crystal fibers and mathematical physics. [ABSTRACT FROM AUTHOR]

The current article aims to discuss the natural convection heat transfer of Ag/Al2O3-water hybrid filled in an enclosure subjected to a uniform magnetic field and provided with a rotating cylinder and an inner undulated porous layer. The various thermo-physical parameters are investigated such as Rayleigh number ( 100 ≤ R a ≤ 100000 ), Hartmann number ( 0 ≤ H a ≤ 100 ), and the nanoparticles concentration ( 0.02 ≤ ϕ ≤ 0.08 ). Likewise, the rotational speed of the cylinder ( - 4000 ≤ ω ≤ + 4000 ), as well as several characteristics related to the porous layer, are examined li its porosity ( 0.2 ≤ ε ≤ 0.8 ), Darcy number ( - 100000 ≤ D a ≤ - 100 ) which indicates the porous medium permeability and the number of undulations ( 0 ≤ N ≤ 4 ). The calculations are carried out based on the Galerkin Finite element method (GFEM) to present the streamlines, isotherms, entropy generation, and average Nusselt numbers in details. The main results proved that increment of Rayleigh number and Darcy number enhances heat transfer convection within the enclosure. Whilst, the porosity presents a minimal impact. Also, the rotational speed in a positive direction has a favorable influence on the heat transfer dispersion across the cavity. [ABSTRACT FROM AUTHOR]

A novel hybrid nanofluid was explored in order to find an efficient heat-transmitting fluid to replace standard fluids and revolutionary nanofluids. By using tangent hyperbolic hybrid combination nanoliquid with non-Newtonian ethylene glycol (EG) as a basis fluid and a copper (Cu) and titanium dioxide (TiO2) mixture, this work aims to investigate the viscoelastic elements of the thermal transferring process. Flow and thermal facts, such as a slippery extended surface with magnetohydrodynamic (MHD), suction/injection, form factor, Joule heating, and thermal radiation effects, including changing thermal conductivity, were also integrated. The Keller–Box method was used to perform collective numerical computations of parametric analysis using governing equivalences. In the form of graphs and tables, the results of TiO2–Cu/EG hybrid nanofluid were compared to those of standard Cu/EG nanofluid in important critical physical circumstances. The entropy generation study was used to examine energy balance and usefulness for important physically impacting parameters. Detailed scrutiny on entropy development get assisted with Weissenberg number, magnetic parameter, fractional volumes, injection parameter, thermal radiation, variable thermal conductivity, Biot number, shape variation parameter, Reynolds and Brinkman number. Whereas the entropy gets resisted for slip and suction parameter. In this case, spotted entropy buildup with important parametric ranges could aid future optimization. [ABSTRACT FROM AUTHOR]

Prandtl–Eyring hybrid nanofluid (P-EHNF) heat transfer and entropy generation were studied in this article. A slippery heated surface is used to test the flow and thermal transport properties of P-EHNF nanofluid. This investigation will also examine the effects of nano solid tubes morphologies, porosity materials, Cattaneo–Christov heat flow, and radiative flux. Predominant flow equations are written as partial differential equations (PDE). To find the solution, the PDEs were transformed into ordinary differential equations (ODEs), then the Keller box numerical approach was used to solve the ODEs. Single-walled carbon nanotubes (SWCNT) and multi-walled carbon nanotubes (MWCNT) using Engine Oil (EO) as a base fluid are studied in this work. The flow, temperature, drag force, Nusselt amount, and entropy measurement visually show significant findings for various variables. Notably, the comparison of P-EHNF's (MWCNT-SWCNT/EO) heat transfer rate with conventional nanofluid (SWCNT-EO) results in ever more significant upsurges. Spherical-shaped nano solid particles have the highest heat transport, whereas lamina-shaped nano solid particles exhibit the lowest heat transport. The model's entropy increases as the size of the nanoparticles get larger. A similar effect is seen when the radiative flow and the Prandtl–Eyring variable-II are improved. [ABSTRACT FROM AUTHOR]

Micropolar fluids are used in lubrication theory, thrust bearing technologies, cervical flows, lubricants, paint rheology, and the polymer industry. This study develops the numerical simulation of the magneto-Darcy flow of a polarized nanoliquid with Joule heating and viscous heating mechanisms on an exponentially elongated surface. The effects of linearized Rosseland radiation and temperature-dependent heat generation are considered. The flow is generated by an exponential form of elongation of a flexible sheet. The porous matrix and nanoparticle effects are characterized by the Darcy expression and the two-component Buongiorno model correspondingly. The resulting partial differential systems are solved numerically using the Runge–Kutta-based shooting technique to interpret the importance of key parameters in physical quantities. A direct comparison is made to validate the results. Our results demonstrated that arbitrary movement of the nanoparticles significantly advances the temperature profile by reducing the concentration of nanoparticles. Both Joule heating and viscous heating mechanisms improve the structure of the thermal boundary layer. The porous matrix reduces the velocity of the nanoliquid and thus the width of the velocity boundary layer is reduced. [ABSTRACT FROM AUTHOR]

The present investigation involves the Hall current effects past a low oscillating stretchable rotating disk with Joule heating and the viscous dissipation impacts on a Ferro-nanofluid flow. The entropy generation analysis is carried out to study the impact of rotational viscosity by applying a low oscillating magnetic field. The model gives the continuity, momentum, temperature, magnetization, and rotational partial differential equations. These equations are transformed into the ODEs and solved by using bvp4c MATLAB. The graphical representation of arising parameters such as effective magnetization and nanoparticle concentration on thermal profile, velocity profile, and rate of disorder along with Bejan number is presented. Drag force and the heat transfer rate are given in the tabular form. It is comprehended that for increasing nanoparticle volume fraction and magnetization parameter, the radial, and tangential velocity reduce while thermal profile surges. The comparison of present results for radial and axial velocity profiles with the existing literature shows approximately the same results. [ABSTRACT FROM AUTHOR]

In this work, a numerical scheme based on combined Lucas and Fibonacci polynomials is proposed for one- and two-dimensional nonlinear advection–diffusion–reaction equations. Initially, the given partial differential equation (PDE) reduces to discrete form using finite difference method and θ - weighted scheme. Thereafter, the unknown functions have been approximated by Lucas polynomial while their derivatives by Fibonacci polynomials. With the help of these approximations, the nonlinear PDE transforms into a system of algebraic equations which can be solved easily. Convergence of the method has been investigated theoretically as well as numerically. Performance of the proposed method has been verified with the help of some test problems. Efficiency of the technique is examined in terms of root mean square (RMS), L 2 and L ∞ error norms. The obtained results are then compared with those available in the literature. [ABSTRACT FROM AUTHOR]

Survey of literature unveils that nanofluids are more efficient for heat transport in comparison to the traditional fluids. However, the enlightenment of developed techniques for the augmentation of heat transport in nanomaterials has considerable gaps and, consequently, an extensive investigation for aforementioned models is vital. The ongoing investigation aims to study the 2-D, incompressible Jeffrey nanofluid heat transference flow due to a stretchable surface. Furthermore, the effect of dispersion of graphene nanoparticles in base liquid ethylene glycol (EG) on the performance of flow and heat transport using the Tawari-Das model in the existence of Ohmic heating (electroconductive heating) and viscous heat dissipation is contemplated. The boundary-layer PDEs are reconstituted as ODEs employing appropriate similarity transformation. Keller-Box Method (KBM) is utilized to determine the numerical findings of the problem. Graphene conducts heat greater in rate than all of the other materials and it is a good conductor of electrical energy. Graphene/EG nanofluid is employed to look out the parametric aspects of heat transport flow, drag coefficient, and heat transference rate phenomena with the aid of graphs and tables. The numerical outcomes indicate that concentration and magnetic field abate the shear stresses for the nanofluid. An increase of Graphene nanoparticle volume fraction parameter can boost the heat transport rate. The effect of Prandtl Number is to slow down the rate of heat transport as well as decelerate the temperature. Additionally, the rate of heat transportation augments on a surface under Deborah's number. Results indicate that the temperature of the graphene-EG nanofluid is greater than the convectional fluid hence graphene-EG nanofluid gets more important in the cooling process, biosensors and drug delivery than conventional fluids. [ABSTRACT FROM AUTHOR]