Aboodh Transform Homotopy Perturbation Method For Solving System Of Nonlinear Partial Differential Equations

In this paper, we apply a new method called Aboodh transform homotopy perturbation method (ATHPM) to solve nonlinear systems of partial differential equations. This method is a combination of the new integral transform “Aboodh transform” and the homotopy perturbation method. This method was found to be more effective and easy to solve linear and nonlinear differential equations. Key word:Aboodh  transform Homotopy  perturbation  method Nonlinear  systems  of  partial differential equation

A New Approach in Solving Regular and Singular Conformable Fractional Coupled Burger's Equations

The conformable double ARA decomposition approach is presented in this current study to solve one-dimensional regular and singular conformable functional Burger's equations. We investigate the conformable double ARA transform's definition, existence requirements, and some basic properties. In this study, we introduce a novel interesting method that combines the double ARA transform with Adomian's decomposition method, in order to find the precise solutions of some nonlinear fractional problems. Moreover, we use the new approach to solve Burgers' equations for both regular and singular conformable fractional coupled systems. We also provide several instances to demonstrate the usefulness of the current study. Mathematica software has been used to get numerical results

ARA-Homotopy Perturbation Technique with Applications

In this study, we propose a novel combination method between the ARA integral transform and the homotopy perturbation approach to solve systems of nonlinear partial differential equations. The difficulty arising in solving nonlinear partial differential equations could simply be overcome by using He’s polynomials during the application of the new method. The proposed technique can provide the solutions of the target problems without pre-assumptions or restrictive constrains in addition to avoiding the round-off errors. The efficiency of the new method is illustrated by applying it to solve different examples of systems of nonlinear partial differential equations. We discuss three interesting applications and solve them by the new approach, called ARA-homotopy perturbation method and get exact solutions, also the results are illustrated in figures

Double Formable Integral Transform for Solving Heat Equations

Chemistry, physics, and many other applied fields depend heavily on partial differential equations. As a result, the literature contains a variety of techniques that all have a symmetry goal for solving partial differential equations. This study introduces a new double transform known as the double formable transform. New results on partial derivatives and the double convolution theorem are also presented, together with the definition and fundamental characteristics of the proposed double transform. Moreover, we use a new approach to solve a number of symmetric applications with different characteristics on the heat equation to demonstrate the usefulness of the provided transform in solving partial differential equations