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In this article, the plane Poiseuille flow of couple stress fluid of Vogel’s model between two parallel plates under the influence of non-isothermal effects have been investigated using Optimal homotopy asymptotic method (OHAM) and New iterative method (NIM). The governing continuity and momentum equations are transformed to ordinary differential equations and the coupled system of differential equations is then explored using the said methods. The expressions for velocity profile, temperature distribution, average velocity, volume flux, and shear stress have been obtained employing the said methods. Various essential flow properties have been presented and discussed. The results acquired via these techniques are in the form of infinite series; thus, the results can be effortlessly calculated. Comparison of both techniques are illustrated with the help of different tables and graphs and found both methods to be in a good agreement. Consequently, it will be more appealing for the investigators to apply the proposed methods to diverse problems arising in fluid dynamics.

In this article, the solution to the time-fractional Fisher equation is determined using two well-known analytical techniques. The suggested approaches are the new iterative method and the optimal auxiliary function method, with the fractional derivative handled in the Caputo sense. The obtained results demonstrate that the suggested approaches are efficient and simple to use for solving fractional-order differential equations. The approximate and exact solutions of the partial fractional differential equations for integer order were compared. Additionally, the fractional-order and integer-order results are contrasted using simple tables. It has been confirmed that the solution produced using the provided methods converges to the exact solution at the appropriate rate. The primary advantage of the suggested method is the small number of computations needed. Moreover, it may be used to address fractional-order physical problems in a number of fields.

In this article, we used a novel semi-analytical approach, named the optimal auxiliary function method (OAFM), to solve integro-differential equations (IDEs). The OAFM includes an auxiliary function and convergence control parameters, which expedite the convergence of the method. To apply the proposed method, some assumptions regarding small or large parameters in the problem are necessary. We present numerical outcomes acquired via the OAFM alongside those obtained from other numerical techniques in tables. Furthermore, we demonstrate the efficacy and ease of implementing the proposed method for various IDEs using 2D graphs.

In this article, natural transform iterative method has been used to find the approximate solution of fractional order parabolic partial differential equations of multi-dimensions together with initial and boundary conditions. The method is applicable without any discretization or linearization. Three problems have been taken as test examples and the results are summarized through plots and tables to show the efficiency and reliability of the method. By practice of a few iterations, we observe that the approximate solution of the parabolic equations converges to the exact solution. The fractional derivatives are considered in the Caputo’s sense.

The aim of this study is to investigate the numerical analysis of an innovative model containing, bioconvection phenomena with a gyrotactic motile microorganism of magnetohydrodynamics Williamson nanofluids flow along with heat and mass transfer past a stretched surface. The effect of thickness variation and thermal conductivity feature is employed in the model. Bioconvection in nanofluid helps in bioscience such as in blood flow, drug delivery, micro-enzyme, biosensors, nanomedicine, for content detection, etc. For simulation procedure, the mathematical partial differential equations are converted into dimensionless systems owing to dimensionless variations such as magnetic field, power index velocity, Williamson parameter, wall thickness parameter, thermal conductivity variation, Prandtl number, thermal radiation, Brownian motion, Lewis number, Peclet number, and different concentration parameter, etc. For numerical simulation, New Iterative Technique (NIM) numerical algorithm is adopted and employed for the linear regression planned for the proposed model. For comparison purposes, the homotopy technique is employed on the flow model. Close agreement is seen between both methods revealing the accuracy and consistency of NIM numerical technique. Many features of no-scale constraints are evaluated through graphical data for a key profile of the flow model. Results show that microorganism concentration is heavy due to the magnetic effect and Hall current.

In this paper, the implementation of the Fractional Variational iteration method (FVIM) is used to approximate the generalized fractional perturbed Zakharove-Kuznetsov equation. The obtained results show that the suggested approach is very efficient for dealing with various forms of differential equations of fractional order. The numerical comparison for the attained resolution is made through the q-homotopy analysis transmute manner (q-HATM) which confirms the convergence of the devised method. The applicability of the method is observed by applying the proposed technique to two numerical examples. Furthermore, the solutions obtained by the FVIM are completely well-matched with the solutions presented in the literature. [ABSTRACT FROM AUTHOR]

In this article, the generalized plane Couette flow of Vogel’s model of incompressible, non-isothermal, couple stress fluid flowing steadily between two parallel walls is investigated. The governing equations are reduced to ordinary differential equations. To investigate the non-linear coupled system of differential equations, the optimal homotopy asymptotic method with DJ polynomial and asymptotic homotopy perturbation method have been used. Important flow properties are presented and discussed. We have obtained expressions for velocity, average velocity, shear stress, volume flux and temperature. The results gained employing these techniques are in the form of infinite series; thus, the results can be easily calculated. Comparison of various results, obtained through the suggested approaches, is carried out and an excellent agreement is achieved.

In this paper, the approximate solution of time fractional coupled Jaulent-Miodek equation has been found using q-Homotopy Analysis Method (q-HAM) with the help of Fractional Complex Transformation (FCT). Fractional derivative are described in the Caputo sense. Results obtained by (q-HAM) are compared with two dimensional Hermite Wavelet method. Results of the proposed method admit a remarkable accuracy over two dimensional Hermite Wavelet method. The accuracy of (q-HAM) increases as we increase the value of n as shown in the paper. All calculation are presented with the use of Mathematica. For n = 1 (q-HAM) reduces to Homotopy Analysis Method (HAM). [ABSTRACT FROM AUTHOR]

The present study aims to perform a comparative analysis of the plane Couette flow of a couple stress fluid under the influence of magnetohydrodynamics (MHD) using two different methods: the Optimal Auxiliary Function Method (OAFM) and the Homotopy Perturbation Method (HPM). The couple stress fluid is known for its non-Newtonian behavior, where the fluid's response to shear is influenced by the presence of internal microstructure. The OAFM and HPM are utlized to solve the governing equations of the couple stress fluid flow under MHD. The OAFM is a numerical technique that involves introducing an auxiliary function to simplify the equations, leading to an easier solution procedure. On the other hand, HPM is an analytical method that employs a series solution. The comparative analysis focuses on examining the accuracy, efficiency, and convergence behavior of the two methods. Various flow parameters such as the couple stress parameter, the magnetic parameter, and the velocity ratio are considered to investigate their influence on the flow behavior. Furthermore the HPM solution was compared with the OAFM solution using different graphs and tables. It reveals that the solution obtained by HPM is batter than OAFM solution. [ABSTRACT FROM AUTHOR]

In this paper, the Poiseuille flow of non-isothermal couple stress fluid of Reynolds model between two heated parallel inclined plates has been studied. The strongly nonlinear coupled ordinary differential equations have been investigated using the Asymptotic Homotopy Perturbation method (AHPM) and the Optimal Homotopy Asymptotic Method with DJ Polynomials (OHAM-DJ). Employing both these techniques, the approximate solutions for velocity profile, temperature distributions, shear stress, average velocity and volumetric flow rate have been achieved. The results obtained using both these methods are in the form of infinite series, hence the results can be obtained easily. Comparison of various results, obtained through these methods, is carried out. Here, it is worth to mention that the results gained by both these approaches are in excellent resemblance. The effect of different parameters on the flow problem has been studied numerically as well as presented graphically. [ABSTRACT FROM AUTHOR]

Within the context of fractional calculus, we investigate novel mathematical possibilities. In this context, using the fractional dispersion relations for the fractional wave equation, we explore a class of the generalized fractional wave equation numerically. Some important classes of differential equations in the theory of wave studies are Drinfeld–Sokolov–Wilson and Shallow Water equations. In this effort, the natural transform decomposition technique has been implemented to investigate the explicit result of fractional-order coupled schemes of Drinfeld–Sokolov–Wilson and Shallow Water coupled systems. The proposed method is obtained by coupling the Natural transform with the Adomian decomposition process. The current technique significantly works to find the approximate solution without any discretization or constraining parameter assumptions. The obtained numerical and graphical outcomes by the devised technique are compared with the available exact result to verify the convergence of the method. For mathematical calculations, the Mathematica software package is used. [ABSTRACT FROM AUTHOR]