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This study aims to analyze the two-dimensional incompressible, steady MHD-mixed convective nanofluid flow with homogenous–heterogeneous (hh) reaction and Cattaneo–Christov heat flux (CCHF) past a rotating cone. The uniqueness of the presented model is the consideration of the surface-catalyzed reaction while considering the hh reactions on the surface of the cone in the existence of a permeable medium. Owing to this supposition, the rate of reaction is provoked in the least possible time. Moreover, irreversibility analysis is also performed for the suggested mathematical model in the wake of the second law of thermodynamics. The impacts of slip conditions and heat sink/source are also assessed here. The numerical model of these governing equations is solved using the MATLAB bvp4c package that addresses the system of ODES extracted from the governing PDEs. Graphs are used to evaluate the important consequences of the main arising parameters versus the concerned fields. The results revealed that in the presence of a high magnetic field, the temperature is enhanced. Moreover, the Entropy generation is boosted for magnetic and diffusion parameters. The results presented for this model are also corroborated by associating them with the published study. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the approximate controllability of fractional stochastic delay differential inclusions of order r ∈ (1 , 2). By using fractional calculus, stochastic analysis, the theory of cosine family and Dhage fixed point techniques, a new set of necessary and sufficient conditions are formulated which guarantees the approximate controllability of the nonlinear fractional stochastic system. In particular, the results are established with the assumption that the associated linear part of the system is approximately controllable. Further, the result is extended to obtain the conditions for the solvability of controllability results for fractional inclusions with nonlocal conditions. Finally, an example is presented to illustrate the theory of the obtained result. [ABSTRACT FROM AUTHOR]

The main motivation of our conversation is the existence and approximate controllability for fractional stochastic Volterra–Fredholm integro-differential systems having order 1 < r < 2. The primary outcomes are obtained by applying concepts and ideas from fractional calculus, multivalued maps, the theory of cosine family, Martelli and Dhage, and Leray–Schauder fixed point techniques. We begin by emphasizing the existence, and then demonstrate the approximate controllability of the considered system. Additionally, we determine the approximate controllability outcomes for the system with infinite delay. At last, an application is established for drawing the theoretical conclusions of primary outcomes. [ABSTRACT FROM AUTHOR]

The objective of this paper is to set up some finite integral formulas involving the generalized Bessel first kind function negative order of m, modified Bessel function and spherical Bessel function. The result is given in terms of generalized Wright's Hypergeometric functions pΨq. These results are procured with the help of finite integral due to Lavoie and Trottier. Some interesting particular cases in terms of corollary are established here. [ABSTRACT FROM AUTHOR]

This study investigates the functional abstract second order impulsive differential equation with state-dependent delay. The major result of this study is that the abstract second-order impulsive differential equation with state-dependent delay system has at least one solution and is unique. After that, the wellposed condition is defined. Following that, we look at whether the proposed problem is wellposed. Finally, some illustrations of our findings are provided. [ABSTRACT FROM AUTHOR]

In this exploration, temperature-dependent Yamada–Ota and Xue hybrid nanoliquid models are investigated over a curved stretchable surface embedded in an absorbent media. Hybrid nanofluids are formed by the combination of single and multi-walled carbon nanotubes (CNTs) as nanoparticles with engine oil as base fluid. The goal of this study is to interpret how the modified Fourier law combined with temperature-dependent thermal conductivity, Newtonian heating and variable heat source/sink enhances thermal performance. A mathematical formulation of the problem is illustrated in the curvilinear coordinates. Highly nonlinear dimensionless ODEs are solved numerically by engaging the bvp4c approach. The impression of the key parameters is illustrated graphically. Drag force coefficient and Nusselt number are highlighted through tables. It is comprehended that the fluid velocity decays on augmenting the velocity slip parameter while elevates on amplifying the curvature parameter. Furthermore, an enhancement in the temperature field is noted for the conjugate parameter. A significant correlation with the existing outcomes is perceived when a comparison with the existing literature is made. [ABSTRACT FROM AUTHOR]

Recently, Atangana proposed new operators by combining fractional and fractal calculus. These recently proposed operators, referred to as fractal–fractional operators, have been widely used to study complex dynamics. In this paper, the COVID-19 model is considered via Atangana–Baleanu fractal-fractional operator. The Lyapunov stability for the model is derived for first and second derivative. Numerical results have developed through Lagrangian-piecewise interpolation for the different fractal–fractional operators. We develop numerical outcomes through different differential and integral fractional operators like power-law, exponential law, and Mittag-Leffler kernel. To get a better outcome of the proposed scheme, numerical simulation is made with different kernels having the memory effects with fractional parameters. [ABSTRACT FROM AUTHOR]

This paper will introduce novel techniques for a fractional-order model of the human liver involving the Atangana–Baleanu, Atangana–Toufik, and the Fractal fractional method with the nonsingular kernel. These techniques give more accurate and appropriate results. Existence and uniqueness have been developed with the help of fixed-point theory results. Numerical simulations are done from the developed algorithm of the model to elaborate the effect of fractional values and justify the theoretical results. Such kind of analysis will be useful for further investigation of epidemic diseases, and also provide a better understanding of disease dynamics to overcome the effect of disease in a community. [ABSTRACT FROM AUTHOR]

In the cultivation of Capsicum annuum (C. annuum), the major obstacles are triggered by the Yellow virus (Gemini virus). The virus is spread through insects, namely Bemisia tabaci (B. tabaci). To reduce the spreading of the virus in C. annuum, the entomopathogenic fungi (Verticillium lecanii) are used. We have analyzed the fractional-order model of chili plants with Atangana–Baleanu derivative (AB-derivative). Also, we calculate the numerical values to illustrate the results. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids (HNFs) are a new breed of nanofluids that possess numerous tempting applications encompassing microfluidics, transportation, defense, medical, etc. The objective of this novel exploration is to inspect the behavior of Hamilton–Crosser (H-C) and Yamada–Ota (Y-O) HNF flow models past a stretching cylinder. The H-C model is also used to gauge which particle shape (blade, platelet, cylinder, brick) is more effective in the improvement of the heat transfer rate. The envisioned flow is influenced by the Hall current, Cattaneo–Christov (C-C) heat flux and variable thermal conductivity (TC). The uniqueness of the projected model is the notion of a heterogeneous reaction sprouting on the surface of the cylinder in the presence of an absorbent medium. Owing to this supposition, the chemical reaction occurs in the least possible time. The proposed model's novelty lies in the consideration of the surface catalyzed reaction in the HNF flow models past a stretching cylinder amalgamated with the unique impacts of the Hall current, C-C heat flux and variable TC. The thermal performance of the two renowned models H-C and Y-O is also evaluated. The MATLAB software bvp4c technique is used for numerical outcomes of this coupled system. The analysis depicts that the performance of the Y-O HNF flow model is far above the H-C HNF flow model. It is also inferred from the results that blade-shaped nanoparticles possess higher TC than the other nanoparticles. The heat transfer rate for blade-shaped nanoparticles is stronger than the other nanoparticles. The fluid concentration reduces for higher surface-catalyzed reaction parameter. The corroboration of the proposed model is also given in this study. The comparative results disclosed that in the case of the magnetic parameter M , the minimum error percentage is 0.015% for M = 0. 5 , and permeability parameter λ , the least error percentage is 0.037% for λ = 1. 0. [ABSTRACT FROM AUTHOR]

Chemical kinetics is a branch of chemistry that is founded on understanding chemical reaction rates. Chemical kinetics relates many aspects of cosmology, geology, and even in some cases of, psychology. There is a need for mathematical modelling of these chemical reactions. Therefore, the present research is based on chemical kinetics-based modelling and dynamics of enzyme processes. This research looks at the two-step substrate-enzyme reversible response. In the two step-reversible reactions, substrate combines with enzymes which is further converted into products with two steps. The model is displayed through the flow chart, which is then transformed into ODEs. The Atangana-Baleanu time-fractional operator and the Mittag-Leffler kernel are used to convert the original set of highly nonlinear coupled integer order ordinary differential equations into a fractional-order model. Additionally, it is shown that the solution to the investigated fractional model is unique, limited, and may be represented by its response velocity. A numerical scheme, also known as the Atangana-Toufik method, based on Newton polynomial interpolation technique via MATLAB software, is adopted to find the graphical results. The dynamics of reaction against different reaction rates are presented through various figures. It is observed that the forward reaction rates increase the reaction speed while backward reaction rates reduce it. [ABSTRACT FROM AUTHOR]

In this article, the Levenberg-Marquardt back propagation technique under the framework of neural networks (LMBT-NN) is incorporated. The heat and mass transfer characteristics of nanofluid (HMT-CNF) in a magneto-hydrodynamic (MHD) boundary layer over a vertical cone under convective boundary conditions have been investigated. The similarity transformation has been employed with the goal of transforming nonlinear partial differential equations (PDEs) into the system of ordinary differential equations (ODEs). A set of suggested data (LMBT-NN) is produced for some scenarios by modifying the radiation parameter (R), magnetic field parameter (M), buoyancy ratio parameter (Nr), chemical reaction parameter (Cr), thermophoresis factor (Nt), Lewis number (Le), and Brownian motion factor (Nb) within the applicability of the state-of-the-art Adams numerical technique. Using the (LMBT-NN) training, testing, and validation technique, the approximate solution of distinct instances has been validated, and for excellence, the proposed model has equated. To justify the proposed methodology (LMBT-NN), different error plots and numerical illustrations based on mean square errors, histogram plots, and regression analysis representations are prepared. With a correctness level ranging from E-9 to E-10, the recommended method has been observed based on the closeness of the suggested and reference outcomes. [ABSTRACT FROM AUTHOR]

This paper studies a chemical reactive Maxwell nanofluid flow in porous media with generalized Fourier and Fick laws in the presence of temperature-dependent thermal conductivity and robin conditions past a spinning cone. The characteristics of the fluid flow are examined using the Buongiorno nanofluid model. The equations that regulate the flow are highly nonlinear and are simplified using similarity transformations. Numerical solution is obtained by employing the bvp4c technique. The characteristics of various parameters on tangential and azimuthal velocities, heat, and mass transfers are depicted graphically. An opposing behavior on the tangential and azimuthal velocity fields is depicted in elevating the Deborah number. The solutal field upsurges on increasing the order of the reaction. The mass flux strengthens by augmenting the Schmidt number and solutal relaxation time. The validation of the proposed model in the limiting case is also given. [ABSTRACT FROM AUTHOR]

The role of non-Newtonian fluids can't be denied owing to their immense industrial and engineering applications. Taking this point in mind, the motivation of the current investigation is to examine the influence of a magnetic dipole on two-dimensional nonelectrical conducting Oldroyd-B fluid flow in the existence of thermophoretic particle deposition along a linearly stretching surface. The exponential space-based thermal source and the temperature-dependent heat source/sink are incorporated into the thermal equation. The fluid concentration is strengthened with binary activation energy and Arrhenius chemical reaction. The set of ordinary differential equations that are attained after applying the similarity transformations is resolved numerically by the bvp4c approach of MATLAB software. The impact of diverse parameters on velocity, temperature, and concentration are graphically examined. The quantities of physical importance are also computed and analyzed numerically. The results revealed that fluid velocity and temperature have opposing trends for the ferromagnetic interaction parameter. It is also witnessed that the fluid concentration arguments for the chemical reaction parameter. The validation of the model in the limiting case is also given. [ABSTRACT FROM AUTHOR]

This paper is related to some qualitative results about the existence and uniqueness of a solution to a third-order problem by using a fixed point approach. Haar technique is applied for numerical solution of a third-order linear integro-differential equation (IDE) with initial conditions. In IDE, the third-order derivative is computed by Haar functions, and the integration is used to get the expression of second- and first-order derivatives, as well as an approximate solution. Some examples from the literature are used to verify the validity of the proposed method. Error analysis is performed. Also, comparison between the exact and numerical solutions at different collocation points (CPs) is derived. The convergence rate is recorded taking different numbers of CPs, which is approximately equal to 2. [ABSTRACT FROM AUTHOR]

A numerical method for the solution of nonlinear variable-order (VO) fractional differential equations (FDEs) is proposed in this paper. To determine the numerical solution of nonlinear VO FDEs, we used the Haar wavelet collocation method (HWCM) with a combination of Caputo fractional derivatives. For checking the efficiency of the HWCM, some examples are given. The maximum absolute error and mean square root errors of each test problem are computed for a different number of collocation points (CPs) to check the validity and applicability of the presented technique. The comparison of the exact and approximate solution is shown in figures for various numbers of CPs. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids (HNF) are the advanced form of nanofluids used for improved heat transfer purposes. Taking this point in mind, the objective of the presented endeavor is to examine the Yamada–Ota HNF flow model comprising (gold–silver/engine oil) over a stretched cylindrical surface and a sheet (as a limiting case) in a permeable medium. The novelty of this research is the consideration of the surface-catalyzed reaction along with the homogeneous–heterogeneous reactions to accelerate the chemical reactions in the shortest possible time. The heat transport phenomenon is strengthened with the support of Joule heating, heat absorption/generation, and the convective heat boundary condition at the surface of the cylinder. The obtained ordinary differential equations are reduced from the partial differential equations using boundary layer theory and are numerically computed using the Keller box method. It is witnessed that for varied estimates of the magnetic parameter, the thermal profile enhances while the velocity field reduces. It is also noted that the fluid concentration is reduced when the surface-catalyzed parameter is enhanced. The validation of the envisioned model in a limiting case is also added to this investigation. [ABSTRACT FROM AUTHOR]

This article presents, for the first time, a comparative analysis of two different solution methodologies for the numerical investigation of flow and thermal behavior of Casson fluid through a channel having linearly extending lower wall while the upper wall is kept at rest. MHD Casson fluid boundary layer flow is supposed to be steady, laminar, viscous, and incompressible. We have taken into account the mixed convection effects, whereas the usual no slip condition has been imposed on both walls. The Navier–Stokes equations for the proposed model have been converted into nonlinear and coupled system of ordinary differential equations (ODEs) by employing similarity variables, which are then solved by using the differential transform method (DTM) and the quasi‐linearization method (QLM). We note that the quasi‐linearization approach is better than the DTM, as the latter becomes inappropriate for the increasing values of the parameters involved. Moreover, the variation of the different parameters for velocity and temperature profiles has been analyzed graphically. [ABSTRACT FROM AUTHOR]

A mathematical model revealing the transmission mechanism of COVID-19 is produced and theoretically examined, which has helped us address the disease dynamics and treatment measures, such as vaccination for susceptible patients. The mathematical model containing the whole population was partitioned into six different compartments, represented by the SVEIQR model. Important properties of the model, such as the nonnegativity of solutions and their boundedness, are established. Furthermore, we calculated the basic reproduction number, which is an important parameter in infection models. The disease-free equilibrium solution of the model was determined to be locally and globally asymptotically stable. When the basic reproduction number R 0 is less than one, the disease-free equilibrium point is locally asymptotically stable. To discover the approximative solution to the model, a general numerical approach based on the Haar collocation technique was developed. Using some real data, the sensitivity analysis of R 0 was shown. We simulated the approximate results for various values of the quarantine and vaccination populations using Matlab to show the transmission dynamics of the Coronavirus-19 disease through graphs. The validation of the results by the Simulink software and numerical methods shows that our model and adopted methodology are appropriate and accurate and could be used for further predictions for COVID-19. [ABSTRACT FROM AUTHOR]

This article focuses on magneto hydrodynamic (MHD) secretion of secondary fluid in an expanded area. The dominant type is controlled by suction (injection) and viscous discharge. The Tiwari‐Das nanofluid model is the primary reference for the governing model. The final equations obtained from this model are solved by implementing the shooting technique, where this technique contains a fourth‐order method of the Runge‐Kutte method. In addition, the final values (in standard ODE divisions) are produced out of statistical parameters (PDEs) that guided the governing model at the start. The variations for all parameters are demonstrated through visual solutions. It has been found that the distribution of thermal energy decreases as the solid volume fraction rises, but velocity decreases in conjunction. The temperature of the fluid and the Nusselt number rise as Bs$Bs$ values are enhanced. The Nusselt number and temperature distribution are affected by rising values of Nr$Nr$ and Ec$Ec$. [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]

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 sensitivity analysis and response surface methodology (RSM) is performed for the key parameters governed by the magneto‐flow and heat transport of the Carreau nanofluids model toward a stretching/shrinking surface in the presences Arrhenius activation energy and chemical reaction. Nanofluid that displayed Brownian motion and thermophoresis was considered with the permeable condition. The effects of different physical parameters were analyzed by employing appropriate similarity transformations in nonlinear partial differential equations and converted to the dimensionless system of ordinary differential equations. The finite difference method in bvp4c code solves the equations numerically. Associated parameters are presented graphically and interpreted against local Nusselt number, Sherwood number, and skin friction coefficient. An increase in the activation energy factor leads to increased concentration in permeable flow. The higher the activation energy lower the temperature and causes the reaction rate constant to decrease. In addition, it slows down the chemical reaction and increases the concentration characteristics. The increase of radiation and Prandtl number leads to an increase in heat transfer for the permeable surface. Furthermore, the Schmidt number and the binary reaction rate parameter increase the mass transfer for suction/injection flow. As a result, the Nusselt number's highest sensitivity is the Eckert number and the lowest to the thermophoresis parameter. The Sherwood number's positive sensitivity is observed for the Eckert number and Brownian motion parameter, whereas negatively sensitive to thermophoresis. [ABSTRACT FROM AUTHOR]

It is well known that solar energy is the main source of thermal energy coming from the sun responsible for huge operations in engineering studies. It can be seen in the technology of photovoltaic cells, solar streetlights, solar energy plates, and solar water pumping. This study is for investigating solar radiation as well as a method to improve the performance of the solar water pump (SWP) with the use of solar radiation along with nanotechnology. The thermal transfer performance of the pump is checked for the case of many impacts including heat radiations and variable thermal conductivity. An Oldroyd‐B nanofluid with entropy production analysis has been scrutinized as a working coolant liquid in the system. Graphene oxide (GO) and Cu nanoparticles have been employed in engine oil (EO) as the base liquid. It is noticed that the heat transfer performance of SWP increases in the case of amplification in thermal radiation and temperature‐dependent thermal conductivity characteristics. In comparison to low thermal conductivity nanofluid, high thermal conductivity nanofluid provides the best capability for heat transmission. The thermal efficiency of the used (GO/EG) nanofluid has been enhanced by between 7.70% and 26.68% than (Cu/EO) nanofluid. [ABSTRACT FROM AUTHOR]

The objective of this work is to explore the flow features and thermal radiation properties of the 2-D Magnetohydrodynamic (MHD) Carreau nanofluid model over an impenetrable stretching surface by utilizing the supervised learning strength of Levenberg–Marquardt backpropagation neural networking technique (LMBNNT). The mathematical formulation for MHD Carreau nanofluid flow model (MHDCNFM) in terms of partial differential equations (PDEs) is transformed into equivalent nonlinear ordinary differential equations (ODEs) by utilizing the similarity transformation and dimensional parameters. A reference dataset of proposed LMBNNT is made for Carreau nanofluid flow model exploiting the strength of Lobatto IIIA technique through the variations of different parameters against the velocity, temperature profile and concentration. These reference datasets are placed for validation, training and testing by LMBNNT and obtained outcomes are compared with reference results to check the accuracy of the designed methodology. The validation of the proposed solution methodology is obtained through the mean square error (MSE), error histogram error profile, regression p lot and fitness plot. MSE values' accuracy is upto 1 0 − 1 0 which establish the reliability of the LMBNNT. Moreover, due to an increase in Weissenberg number, fluid velocity decays in case of shear thinning liquid and higher values of Biot number enhance the temperature profile and improves the rate of heat transfer. Moreover, the increment in Hartman number reduces the surface drag force and large values of Prandtl number reduce the heat transfer process. These results of all these parameters are expressed in well-organized numerical and graphical forms. [ABSTRACT FROM AUTHOR]

Time delays play an important part in modeling the fact that one cannot be communicable for a long time after becoming sick. Delay can be triggered by a variety of epidemiological situations. The most egregious causes of a delay are infection latency in the vector and infection latency in the infected host. The dynamics of susceptible, infected, recovered and cross-immune (SIRC) classed-based model having cross-immune and time-delay in the transmission for spread of COVID-19 abbreviated as (SIRC-CTC-19) are investigated in this study using an intelligent numerical computing paradigm based on the Levenberg–Marquardt Method backpropagated by neural networks (LM-BPNN). The model is mathematically governed by a system of ordinary differential equations that depicts the four nodes as susceptible, infected, recovered and cross-immune ones (SIRC) nodes with cross-immune class and time-delay in transmission components for COVID-19 dissemination (CTC-19). The reference solution of the SIRC model for the spread of COVID-19 is produced by using the explicit Runge–Kutta method for the many scenarios of this model arising from altering delay with regard to time. This reference solution permits the use of evolutionary computing to solve the SIRC-CTC-19 using train, validate and test techniques. The proposed LM-BPNN method's accuracy has been proven by its results overlapping with explicit Runge–Kutta results Calculation of regression metrics, error analysis of histogram illustrations and learning curves on MSE effectively augment the LM-BPNN's accuracy, convergence and reliability in solving the SIRC-CTC-19 model. [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]

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]

The dimensionless coordinates are taken from the standard literature (see [[35]]): HT ht Graph (8)Here, I C i SB 2 sb = - I Bx i + I C i SB 1 sb and I T i SB 2 sb = - I Ax i + I T i SB 1 sb , including I A i and I B i as constants. [Extracted from the article]

To study the dynamical system, it is necessary to formulate the mathematical model to understand the dynamics of various diseases that are spread worldwide. The main objective of our work is to examine neurological disorders by early detection and treatment by taking asymptomatic. The central nervous system (CNS) is impacted by the prevalent neurological condition known as multiple sclerosis (MS), which can result in lesions that spread across time and place. It is widely acknowledged that multiple sclerosis (MS) is an unpredictable disease that can cause lifelong damage to the brain, spinal cord, and optic nerves. The use of integral operators and fractional order (FO) derivatives in mathematical models has become popular in the field of epidemiology. The model consists of segments of healthy or barian brain cells, infected brain cells, and damaged brain cells as a result of immunological or viral effectors with novel fractal fractional operator in sight Mittag Leffler function. The stability analysis, positivity, boundedness, existence, and uniqueness are treated for a proposed model with novel fractional operators. Model is verified the local and global with the Lyapunov function. Chaos Control will use the regulate for linear responses approach to bring the system to stabilize according to its points of equilibrium so that solutions are bounded in the feasible domain. To ensure the existence and uniqueness of the solutions to the suggested model, it makes use of Banach's fixed point and the Leray Schauder nonlinear alternative theorem. For numerical simulation and results the steps Lagrange interpolation method at different fractional order values and the outcomes are compared with those obtained using the well-known FFM method. Overall, by offering a mathematical model that can be used to replicate and examine the behavior of disease models, this research advances our understanding of the course and recurrence of disease. Such type of investigation will be useful to investigate the spread of disease as well as helpful in developing control strategies from our justified outcomes. • The disease transmission dynamics and the creation of control systems are investigated. • The work focuses on neurological disorders using the fractal-fractional Mittag-Leffler (FFM) derivative. • The fixed points of the model are identified and the stability analysis is carried out. • The fractional Lagrange interpolation method is utilized to compute the model's numerical solutions. • Finally, numerical simulations confirm the agreement between the theoretical findings and the numerical results. [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]

The use of hybrid nanoparticles to improve thermal processes is a key method that has implications for a variety of interventions utilized in many sectors. This paper aimed to look into the impacts of ternary nanoparticles on hyperbolic tangent materials to establish their thermal characteristics. Flow describing equations have been explored in the presence of heat production, non-Fourier heat flux, and an induced magnetic field. Boundary layer analysis, which generates partial differential equations, was used to model the physical situation under several major physical properties (PDEs). The flow rheology is expanded and calculated in a rotating frame by supposing that the flow is created by a spinning disk. The solution of complicated generated PDEs was calculated using the Galerkin finite element technique (G-FEM) after translating them into corresponding ODEs. Several major bodily repercussions have been seen and documented because of increasing the implicated influencing factors. Additionally, finite element approaches are provided for approximating the solution of nonlinear system problems encountered in flowing fluid and other computational physics areas. [ABSTRACT FROM AUTHOR]

This manuscript mainly focuses on the exact controllability of Sobolev-type Hilfer fractional neutral delay Volterra-Fredholm integro-differential systems. The principal findings of this discussion are established by using the theories on fractional calculus, the measure of noncompactness and Mönch fixed point technique. Initially, the exact controllability of the system is presented and then we improve the discussion to the system with nonlocal conditions. Finally, abstract and filter systems are provided for the illustration. [ABSTRACT FROM AUTHOR]

In this theory, the existence of a mild solution for a neutral partial integrodifferential nonlocal system with finite delay is presented and proved using the techniques of the Monch–Krasnosel'skii type of fixed point theorem, a measure of noncompactness and resolvent operator theory. For this work, we have introduced some sufficient conditions to confirm the existence of the neutral partial integrodifferential system. An illustration of the derived results is offered at the end with a filter system corresponding to our existence result. [ABSTRACT FROM AUTHOR]

This study emphasizes the performance of two-dimensional electrically non-conducting Oldroyd-B fluid flowing across a stretching sheet with thermophoretic particle deposition. The heat and mass transfer mechanisms are elaborated in the presence of a magnetic dipole, which acts as an external magnetic field. The fluid possesses magnetic characteristics due to the presence of ferrite particles. The gyrotactic microorganisms are considered to keep the suspended ferromagnetic particles stable. Cattaneo–Christov heat flux is cogitated instead of the conventional Fourier law. Further, to strengthen the heat transfer and mass transfer processes, thermal stratification and chemical reaction are employed. Appropriate similarity transformations are applied to convert highly nonlinear coupled partial differential equations into non-linear ordinary differential equations (ODEs). To numerically solve these ODEs, an excellent MATLAB bvp4c approach is used. The physical behavior of important parameters and their graphical representations are thoroughly examined. The tables are presented to address the thermophoretic particle velocity deposition, rate of heat flux, and motile microorganisms' density number. The results show that the rate of heat transfer decreases as the value of the thermal relaxation time parameter surges. Furthermore, when the thermophoretic coefficient increases, the velocity of thermophoretic deposition decreases. [ABSTRACT FROM AUTHOR]

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]

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]

In the present paper, the melting heat transfer of a nanofluid over a stretching sheet is investigated. Magnetohydrodynamic stagnation point flow with thermal radiation and slip effects is considered for this study. The governing model of the flow is solved by Runge–Kutta fourth‐order method using appropriate similarity transformations. Temperature and velocity fields are presented for various flow pertinent parameters. Nondimensional physical parameters such as Prandtl number, radiation parameter, Brownian motion parameter, Lewis number, thermophoresis parameter, magnetic parameter, and melting parameter on fluid velocity, heat, concentration, skin friction, Sherwood number, and Nusselt number are presented graphically and discussed numerically. Heat transfer rate can be increased by increasing slip, melting, or radiation parameter. Mass transfer increases for greater values of melting parameter or slip parameter while radiation parameter shows the opposite impact on mass transfer. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to explore the behavior of Sutterby nanofluid passed a sloping sheet with a tendency to fluctuate thermal conductivity, radiation and a magnetic field. In a solar parabolic trough collector (PTC) for solar cooling and hydrogen generation, a nanofluid is employed as the running fluid. The Koo-Kleinstreuer-Li (KKL) model is used to calculate effective thermal conductivity and viscosity. The advance results are differentiate with the Lobatto 111A method which strengthens the integration reliability of the current liquid system. Copper oxide-engine oil (CuO-EO) is taken into consideration to address the performance analysis of the current study. The skin coefficient and the local Nusselt number are expressed numerically in the form of a table, whereas other dominant competent parameters on the speed and temperature profiles are discussed numerically and graphically. The radiation parameter slows the rate of heat transfer while increasing the velocity gradient. To test the effect on many device performance parameters, nanoparticle absorption also varies with the growth of Reynolds and Brinkman numbers, entropy creates growth. The thermodynamic action of copper oxide-engine oil (CuO-EO) nanofluid is more noticeable than engine oil (EO) nanofluid oil under similar conditions. CuO-based EO nanofluid system had the best heat transmission efficiency and hydrogen generation. The thermal effectiveness of CuO-EO over EO is characterized by a minimum of 2.89% and a magnitude of 14.79%. Written theory simulations may be more effective in developing solar thermal energy systems. • Here Sutterby nanofluid passed a sloping sheet with radiation, and magnetic field is addressed. • Effective thermal conductivity and viscosity by Koo-Kleinstreuer-Li (KKL) model is used. • Copper oxide-engine oil (CuO-EO) with Lobatto 111A method is considered. • Total entropy rate is calculated through second law of thermodynamics. • Device performance is studied via different parameters. [ABSTRACT FROM AUTHOR]

The investigation of existence and uniqueness of impulsive dynamical fractional systems with quadratic perturbation of second type subject to nonlocal boundary conditions is presented and proved. By employing the fractional theory, Banach contraction technique, and Krasnoselskii's fixed point theorem, we derived some sufficient conditions to ensure the existence of our system. An example is offered to enhance the applicability of the results obtained. [ABSTRACT FROM AUTHOR]

In this framework entropy generation optimization in dissipative flow of Ree-Eyring fluid model (EGODF-RFM) with chemical reaction of quartic autocatalysis between two rotating disks is observed by operating the artificial neural networks model backpropagated with Bayesian Regularization technique (ANNM-BBRT). The effects of viscous dissipation and nonlinear thermal radiation on heat transmission are examined. The effects of thermophoresis and Brownian motion are discussed in detail. Entropy generation optimization in nanofluids with homogeneous and heterogeneous chemical reactions is explored in terms of physical features. Partial differential equations of (EGODF-RFM) were transformed to ordinary differential equations using appropriate techniques of similarity conversions. To solve the ODEs and evaluate the reference dataset for ANNM-BBRT, the Homotopy analysis method (HAM) is used. In a MATLAB software this dataset assists to compute the estimated solution of EGODF-RFM. Performance of designed intelligent based computing solver is validated by error histogram, regression analysis, and MSE outcomes. For various parameters, the impacts of flow on the velocity profile, temperature distribution, and concentration profile are investigated. The axial component of velocity is declined with the increase in Weissenberg number but opposite trend is observed in the case of radial and tangential components of velocity. The temperature profile enhances due to higher values of Weissenberg number, thermophoresis parameter, Brownian motion parameter and Eckert number, while the concentration profile associated with the presented fluid flow system is accelerated due to rise of Brownian motion parameter, homogeneous and heterogeneous reaction parameters, respectively. Due to Eckert number, a dual effect is observed for entropy generation and Bejan number, and in the region near the bottom disc, both entropy generation and Bejan numbers are reduced, but their values are gradually improved in the region closer to above disc. Impact of We and Re on the skin friction coefficient is to be observed rising and rate of heat transmission increases as Rd increases, whereas We has the reverse effect. [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]

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]

The main goal of this study is to find solutions for the generalized coupled Ramani equation with the fractional order using the fractional natural decomposition method (FNDM). Four distinct cases are chosen to illustrate and validate the effectiveness of the considered method. The simulations in terms of numeric have been illustrated to confirm the reliability and proficiency of the projected scheme. Moreover, the behavior of the obtained results is captured for distinct fractional order. The comparison study is illustrated to verify the accuracy of the projected procedure. The achieved results exemplify that the projected solution procedure offers a simple algorithm and is also very efficient to analyze the nature of the coupled differential equations with arbitrary order situated in associated areas of Science and Engineering. [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]