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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 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.