Abstract
The main objective of this paper is to improve the optimal homotopy analysis method to find the approximate solutions for the linear and nonlinear partial fractional differential equations. The fractional derivatives are described in the Caputo sense. The optimal homotopy analysis method in applied mathematics can be used for obtaining the analytic approximate solutions for some nonlinear partial fractional differential equations such as the time and space fractional nonlinear Schrödinger partial differential equation and the time and space fractional telegraph partial differential equation. The optimal homotopy analysis method contains the h parameter which controls the convergence of the approximate solution series. Also, this method determines the optimal value of h as the best convergence of the series of solutions.
Highlights
In recent years, there has been a great deal of interest in fractional differential equations
The optimal homotopy analysis method in applied mathematics can be used for obtaining the analytic approximate solutions for some nonlinear partial fractional differential equations such as the time and space fractional nonlinear Schrodinger partial differential equation and the time and space fractional telegraph partial differential equation
The optimal homotopy analysis method contains the h parameter which controls the convergence of the approximate solution series
Summary
Optimal homotopy analysis method for nonlinear partial fractional differential equations Khaled A. This article is published with open access at Springerlink.com
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