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The Schrödinger equation depends on the physical circumstance, which describes the state function of a quantum‐mechanical system and gives a characterization of a system evolving with time. The essential focus of proposed research is to observe the solution for fractional generalized nonlinear Schrödinger (FGNS) equation using q‐homotopy analysis transform method (q‐HATM). The fractional order derivative is taken in the Atangana‐Baleanu (AB) sense. The physical behaviours of achieved solution for FGNS equation are discussed and sketch out graphically. The existence of the solution for the FGNS equation is presented through theorems 4.1 to 4.3. The proposed numerical simulations confirm the advantages of the AB derivative through q‐HATM. Few numerical experiments were carried out to validate the proposed method. Moreover, numerical simulations are carried out to verify efficiency and robustness of the derived results by considering two cases. [ABSTRACT FROM AUTHOR]

The features of ferromagnetic fluids make it supportive for an extensive range of usages in directing magnetic drugs and magnetic hyperthermia. Owing to all such potential applications, the current study is concerned with the ferromagnetic liquid flow past a stretching sheet with thermophoretic particle deposition and a magnetic dipole. The equations of described flow are transformed into ordinary differential equations (ODEs) by selecting suitable similarity variables. These ODEs are later solved numerically by the fourth and fifth-order Runge–Kutta–Fehlberg (RKF-45) technique by using a shooting scheme. The influence of sundry parameters on velocity, thermophoretic diffusive deposition velocity, skin-friction, Nusselt number, Sherwood number, thermal and concentration profiles are illustrated graphically. The results reveal that the increase in ferromagnetic interaction parameter improves the thermal profile but declines the velocity and concentration profiles. The imposition of thermophoretic particle deposition results in declination of the mass transfer. The escalating values of the ferromagnetic interaction parameter decline the rate of heat transfer. Finally, the rise in values of the thermophoretic parameter and thermophoretic coefficient decays thermophoretic diffusive deposition velocity. [ABSTRACT FROM AUTHOR]

This study examines different fluid flow through an elaborated plate. In the modeling of the physical phenomena under investigation, the impacts of viscous dissipation, activation energy and chemical reaction are considered. Also, the heat transport phenomena are explained by the variable thermal conductivity theory. By using the right transformations, the flow-generating PDEs are converted into nonlinear ordinary differential equations. The parameters' impacts on the velocity, temperature and mass fields are analyzed in detail. The modeled problem is graphically handled in MATLAB using the numerical technique (BVP4c). Graphical representations of the important factors affecting temperature and velocity fields are illustrated through graphs. The findings disclose that the effectiveness of the velocity field is determined by the changing values of the magnetic parameter. The Prandtl values are decreased, the temperature profile becomes more pronounced. [ABSTRACT FROM AUTHOR]

In this manuscript, we derive and examine the analytical solution for the solid tumor invasion model of fractional order. The main aim of this work is to formulate a solid tumor invasion model using the Caputo fractional operator. Here, the model involves a system of four equations, which are solved using an approximate analytical method. We used the fixed-point theorem to describe the uniqueness and existence of the model's system of solutions and graphs to explain the results we achieved using this approach. The technique used in this manuscript is more efficient for studying the behavior of this model, and the results are accurate and converge swiftly. The current study reveals that the investigated model is time-dependent, which can be explored using the fractional-order calculus concept. [ABSTRACT FROM AUTHOR]

In this paper, we solved a model of a well-known infectious disease called dengue fever via fractional natural decomposition and modified Predictor–Corrector (PC) methods. A study of the dengue epidemic in the Cape Verde Islands off the coast of West Africa in 2009 has been resumed here for a better understanding of the results. The results are obtained using Liouville–Caputo and new generalized Caputo-type fractional derivatives. The numerical simulations are presented for various orders of given derivatives. Existence and uniqueness analysis of the given problem are also performed in the new generalized Caputo sense. The explored results are verified using figures. The main target of this paper is to explore the different dynamics of the given dengue fever model via two types of fractional numerical algorithms. [ABSTRACT FROM AUTHOR]

The current communication has as its goal the investigation of the flow properties of carbon nanotubes (CNTs) across a stretching surface, which has been accomplished. Furthermore, the effects of radiation, chemical reactions and activation energy are considered. With the use of boundary layer approximations, we can obtain flow expressions. The nondimensional form of flow equations is achieved by applying appropriate transformations. The bvp4c code from MATLAB is used to solve the model that has been obtained. The graphic representation of the relationship between pertinent variables and momentum, temperature field and concentration is used. It is observed that, for larger values of ϕ booms, the micro-rotation distribution. Furthermore, the solutal boundary layer thickness if thinner for thicker values of σ. [ABSTRACT FROM AUTHOR]

Non-Newtonian fluids have industrial and technical applications. Several liquids in nature do not have Newtonian viscosities. These fluids include applesauce, polymer mixtures, colloidal and fermented mixtures, clay glazes, paints, lubricants, cement, slush, shampoos, mud, foodstuffs, paper paste, aqueous froths, etc. This study considers stratified flow and variable heat transmission across a stretched surface. The magnetic hydrodynamics and slips' impacts are illustrated. On the basis of flow assumptions, the mathematical model was created using the Navier–Stokes equation. The boundary layer approximation approach is provided PDEs by working on the Navier–Stokes equation under flow assumptions. This system is converted into ODEs through similarity transformations. Dimensionless system is elucidated by means of RKF-45 technique. The concerning physical parameter effects are elaborated numerically as well as graphically. Based on the findings of the comparison, it was determined that Williamson fluid had superior performance in terms of fluid velocity compared to Maxwell fluid. Furthermore, the temperature of the fluid is greater for booming values of both e 1 and ε parameters. [ABSTRACT FROM AUTHOR]

This work proposes a semi-analytical new hybrid approach, so-called differential -transform method (D TM), to evaluate the behavior of n-space dimensional fractional-nonlinear hyperbolic-like wave equations, where time-fractional derivative is considered in Caputo format. The D TM is the hybrid method in which projected differential transform is implemented after imposing the recently introduced integral transform, i.e., so-called transform [W. Zhao and S. Maitama, J. Appl. Anal. Comput. 10, 1223 (2020)]. The efficiency and applicability of the proposed D TM had been tested by considering three different test examples of the Caputo time-fractional nonlinear hyperbolic-like wave equations in terms of absolute error norms, and the different order D TM solutions are compared with exact solution behaviors and the existing results, for the large time level τ ∈ [ 0 , 1 0 ]. In addition, the convergence analysis of D TM is studied theoretically and verified it numerically as well as graphically, which confirms that the numerical experiments via D TM for distinct fractional orders support the theoretical findings excellently, and the presented D TM results converge to their exact solution behavior, very fast. The evaluated series approximations are expressed in the compact form of Mittag-Leffler functions. [ABSTRACT FROM AUTHOR]

The pivotal aim of the present study is to find the solution for a nonlinear system describing the aggregation process of cellular slime mold by using q -homotopy analysis transform method. The coupled system is considered within the frame of the Caputo fractional operator. We examine three different cases with distinct values of sensitivity function χ ρ = 1 , ρ and ρ 2 to exemplify the efficiency and applicability of the considered scheme. We capture the nature of the obtained results with respect to the fractional order, with distinct initial conditions, and illustrate them using 2D and 3D plots for particular values of the parameters. The considered scheme offers parameters, which help to adjust the convergence region, and we plotted the ℏ-curves to dissipate the effect in the present framework. Moreover, some simulating and important behavior of the considered model using attained results shows the prominence of the hired operator while analyzing the coupled equations and confirms the competence of the projected scheme. [ABSTRACT FROM AUTHOR]

In this paper, the fractional natural decomposition method (FNDM) is employed to find the solution for the KunduEckhaus equation and coupled fractional differential equations describing the massive Thirring model. The massive Thirring model consists of a system of two nonlinear complex differential equations, and it plays a dynamic role in quantum field theory. The fractional derivative is considered in the Caputo sense, and the projected algorithm is a graceful mixture of Adomian decomposition scheme with natural transform technique. In order to illustrate and validate the efficiency of the future technique, we analyzed projected phenomena in terms of fractional order. Moreover, the behaviour of the obtained solution has been captured for diverse fractional order. The obtained results elucidate that the projected technique is easy to implement and very effective to analyze the behaviour of complex nonlinear differential equations of fractional order arising in the connected areas of science and engineering [ABSTRACT FROM AUTHOR]

Squeezing flow of Casson liquid between two disks is a practical application in compression, polymer processing and injection molding. In this paper, the Casson liquid flow between two convectively heated disks is analyzed using Buongiorno model. Further, the heat and mass transport analysis is done by considering the impact of heat source/sink and activation energy. The continuity and momentum equations governing the unsteady two-dimensional flow are derived using conservative laws. The equations are reformulated using the similarity transformations and the reformulated equations are solved numerically with MATLAB routine bvp4c. The effect of embedding different physical parameters on the flow is analyzed through the graphs for both suction and blowing cases along with comprehensive solutions and equal Biot numbers. Results are validated with the existing literature. For both suction and blowing cases, squeezing number decreases the velocity near the lower disk but increases the velocity near the upper disk. Increasing magnetic field strength slightly increases velocity near the lower disk for equal Biot numbers. [ABSTRACT FROM AUTHOR]

The flow of fluid that occurs when two parallel disks are squeezed together has applications in compression, the processing of polymers, the production of plastics, injection modeling, and lubrication systems. In this paper, the unsteady squeezing flow and heat transport of nanoliquid that is subjected to convective thermal boundary conditions and viscous heating have been studied numerically. This study was inspired by the exploration of the thermophysical properties of magnetic nanoparticles in squeezing tribology. The flow between two horizontal parallel disks is accounted for where the upper disk is non-static when the lower disk is fixed. The powerful Runge–Kutta method-based shooting scheme is utilized to solve the assumed problem. The influence of pertinent key parameters on involved fields is visualized graphically and scrutinized. It is exhibited that the haphazard motion of NPs contributes highly to the enhancement of thermal and concentration fields. Also, the Robin boundary conditions affect flow fields significantly. Intensifying the Brownian motion effect enhances NPs' concentration. Radial velocity is damped in the core region with stronger magnetic field. The mass transport rate is diminished, and the heat transmission rate is enhanced. The computations are relevant to smart nano-tribological systems in mechanical and aerospace engineering. [ABSTRACT FROM AUTHOR]

In this paper, we study α-cosymplectic manifold M admitting ∗ -Ricci tensor. First, it is shown that a ∗ -Ricci semisymmetric manifold M is ∗ -Ricci flat and a ϕ -conformally flat manifold M is an η -Einstein manifold. Furthermore, the ∗ -Weyl curvature tensor W ∗ on M has been considered. Particularly, we show that a manifold M with vanishing ∗ -Weyl curvature tensor is a weak ϕ -Einstein and a manifold M fulfilling the condition R E 1 , E 2 ⋅ W ∗ = 0 is η -Einstein manifold. Finally, we give a characterization for α-cosymplectic manifold M admitting ∗ -Ricci soliton given as to be nearly quasi-Einstein. Also, some consequences for three-dimensional cosymplectic manifolds admitting ∗ -Ricci soliton and almost ∗ -Ricci soliton are drawn. [ABSTRACT FROM AUTHOR]

The object of this paper is to study (∈)-Lorentzian para-Sasakian manifolds. Some typical identities for the curvature tensor and the Ricci tensor of (∈)-Lorentzian para-Sasakian manifold are investigated. Further, we study globally φ-Ricci symmetric and weakly φ-Ricci symmetric (∈)-Lorentzian para-Sasakian manifolds and obtain interesting results. [ABSTRACT FROM AUTHOR]

The main purpose of the present investigation is to find the solution of fractional coupled equations describing the romantic relationships using q -homotopy analysis transform method (q -HATM). The considered scheme is a unification of q -homotopy analysis technique with Laplace transform (LT). More preciously, we scrutinized the behavior of the obtained solution for the considered model with fractional-order, in order to elucidate the effectiveness of the proposed algorithm. Further, for the different fractional-order and parameters offered by the considered method, the physical natures have been apprehended. The obtained consequences evidence that the proposed method is very effective and highly methodical to study and examine the nature and its corresponding consequences of the system of fractional order differential equations describing the real word problems. [ABSTRACT FROM AUTHOR]

In this paper we study NMCP manifolds, which are (2p+2q+2)--dimensional differential manifolds with an normal metric contact pair structure. The aim of the study is to examine the Riemannian geometry of normal metric contact pair manifolds under certain conditions related to the *--Ricci tensor. We prove that a *--Ricci-semi-symmetric NMCP manifold is *--Ricci-flat, and that a *--generalized quasi-Einstein NMCP manifold cannot be *--Ricci-semi-symmetric. Finally, we consider the concircular curvature tensor on NMCP manifolds and prove that a concircular flat NMCP manifold is locally isometric to (2p+2q+2)-dimensional hyperbolic space. [ABSTRACT FROM AUTHOR]

In present work, we investigate the numerical solution of time-fractional Jaulent–Miodek (JM) equations with the aid of two novel techniques namely, coupled fractional reduced differential transform method (CFRDTM) and q-homotopy analysis transform method (q-HATM). The obtained solutions are presented in a series form, which are converges rapidly. In order to verify the proposed techniques are reliable and accurate, the numerical simulations have been conducted in terms of absolute error. The obtained solutions are presented graphically to ensure the applicability and validity of the considered algorithms. The results of the study reveal that, the q-HATM is computationally very effective and accurate as compared to CFRDTM to analyse fractional nonlinear coupled JM equations. [ABSTRACT FROM AUTHOR]

The present study examines the approximate solutions of the time fractional Benjamin Bona Mahony Burger equation. This equation is critical for characterizing the dynamics of water waves and fluid acoustic gravity waves, as well as explaining the unidirectional propagation of long waves in nonlinear dispersive systems. This equation also describes cold plasma for hydromagnetic and audio waves in harmonic crystals. The natural transform decomposition method is used to obtain the analytical solution to the time fractional Benjamin Bona Mahony Burger equation. The proposed method uses the Caputo, Caputo Fabrizio, and Atangana Baleanu Caputo derivatives to describe the fractional derivative. We utilize a numerical example with appropriate initial conditions to assess the correctness of our findings. The results of the proposed method are compared to those of the exact solution and various existing techniques, such as the fractional homotopy analysis transform method and the homotopy perturbation transform technique. As a result, bell shaped solitons are discovered under the influence of hyperbolic functions. By comparing the outcomes with tables and graphs, the findings demonstrate the efficacy and effectiveness of the suggested approach., (© 2024. The Author(s).)

It is mentioned that understanding linear and non-linear thermo-elasticity systems is important for understanding temperature, elasticity, stresses, and thermal conductivity. One of the most crucial aspects of the current research is the solution to these systems. The fractional form of several thermo-elastic systems is explored, and elegant solutions are provided. The solutions of fractional and integer thermo-elastic systems are further discussed using tables and diagrams. The closed contact between the LRPSM and exact solutions is displayed in the graphs. Plotting fractional problem solutions demonstrates their convergence towards integer-order problem solutions for suitable modeling. The tables confirm that greater precision is rapidly attained as the terms of the derived series solution increase. The faster convergence and stability of the suggested method support its modification for other fractional non-linear complex systems in nature., (© 2024. The Author(s).)

In this study, brucellosis dynamics between interspecies are discussed with the Atangana-Baleanu fractional derivative to examine the transmission of brucellosis by its behavior. The recovered compartment, recruitment, and natural death rate for humans are considered for the fractional order model to analyze the transmission dynamics in more detail from an epidemiological point of view. Additionally, the saturated incidence rate is suggested for brucellosis as indirectly transmitted to individuals from the environment. By fixed point theory, it is verified that developed fractional transmission dynamics have a unique solution. The model under consideration employs the Adams-type predictor-corrector method for numerical solution. All comparative results are plotted by MATLAB. [ABSTRACT FROM AUTHOR]

In this study, impact of second order slip for Maxwell fluid at vertical exponential stretching sheet is deliberated. Dufour and Soret impact for vertical exponential stretching sheet under nonlinear radiation are deliberated. Thermal and concentration slips with viscous dissipation are taken into account under the Buongiorno's model. Under the above assumptions, the differential model constructed using the boundary layer approximations using the governing equations. The similarities transformations are introduced which applied the differential model (partial differential equations) and developed the dimensionless differential equations (ordinary differential equations). The dimensionless differential equations are cracked by numerical scheme. The impact of physical parameters are presented by tables and graphs. The curves of fluid velocity enhanced due to increasing the values of velocity slip. Velocity slip is a fluid-boundary interaction in physics. If the velocity slip increased, the fluid velocity profile would eventually become increasing. Temperature curves declined by improving values of [Formula: see text]. The thermal thickness reduced when improved the values of [Formula: see text]., (© 2023. The Author(s).)

The main object of the present paper is to discuss about the quarter symmetric metric connection on α-Sasakian Manifold with respect to Ricci Soliton. In this paper, firstly, we discuss the quarter symmetric metric connection on α-Sasakian manifold. Secondly, we elaborate the results of quarter symmetric metric connection on α-Sasakian manifold which admits Ricci Soliton and also flourish a non-trivial example of α-sasakian manifold and validate some of our results. Thirdly, we classify certain curvature properties of Ricci α-Sasakian manifold in regard to Quarter symmetric metric connection. Finally, we show Ricci Soliton on submanifold of α-Sasakian manifold in term of Levi-Civita and quarter symmetric metric connection. [ABSTRACT FROM AUTHOR]

The goal of this research is to develop a new, simplified analytical method known as the ARA-residue power series method for obtaining exact-approximate solutions employing Caputo type fractional partial differential equations (PDEs) with variable coefficient. ARA-transform is a robust and highly flexible generalization that unifies several existing transforms. The key concept behind this method is to create approximate series outcomes by implementing the ARA-transform and Taylor's expansion. The process of finding approximations for dynamical fractional-order PDEs is challenging, but the ARA-residual power series technique magnifies this challenge by articulating the solution in a series pattern and then determining the series coefficients by employing the residual component and the limit at infinity concepts. This approach is effective and useful for solving a massive class of fractional-order PDEs. Five appealing implementations are taken into consideration to demonstrate the effectiveness of the projected technique in creating solitary series findings for the governing equations with variable coefficients. Additionally, several visualizations are drawn for different fractional-order values. Besides that, the estimated findings by the proposed technique are in close agreement with the exact outcomes. Finally, statistical analyses further validate the efficacy, dependability and steady interconnectivity of the suggested ARA-residue power series approach. [ABSTRACT FROM AUTHOR]

The Laplace residual power series (LRPS) method uses the Caputo fractional derivative definition to solve nonlinear fractional partial differential equations. This technique has been applied successfully to solve equations such as the fractional Kuramoto–Sivashinsky equation (FKSE) and the fractional generalized regularized long wave equation (GRLWE). By transforming the equation into the Laplace domain and replacing fractional derivatives with integer derivatives, the LRPS method can solve the resulting equation using a power series expansion. The resulting solution is accurate and convergent, as demonstrated in this paper by comparing it with other analytical methods. The LRPS approach offers both computational efficiency and solution accuracy, making it an effective technique for solving nonlinear fractional partial differential equations (NFPDEs). The results are presented in the form of graphs for various values of the order of the fractional derivative and time, and the essential objective is to reduce computation effort. [ABSTRACT FROM AUTHOR]