In this paper, we will compare a Homotopy perturbation algorithm and Taylor series expansin method for a system of second kind Fredholm integral equations. An application of He’s homotopy perturbation method is applied to solve the system of Fredholm integral equations. Taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

Abstract: In this paper, new algorithm of homotopy analysis method is successfully applied to obtain the approximate analytical solutions of the Cauchy reaction-diffusion equation. Reaction-diffusion equations have special importance in engineering and sciences and constitute a good model for many systems in various fields. Application of new algorithm of homotopy analysis method to this proble...

The aim of this paper is by using the fractional complex transform and the optimal homotopy analysis by method (OHAM) to find the analytical approximate solutions for nonlinear partial fractional differential Zakharov-Kuznetsov equation. Fractional complex transformation is proposed to convert nonlinear partial fractional differential Zakharov-Kuznetsov equation to nonlinear partial differentia...

In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution...