Applying discrete homotopy analysis method for solving fractional partial differential equations

Abstract

In this paper we developed a space discrete version of the homotopy analysis method (DHAM) to find the solutions of linear and nonlinear fractional partial differential equations with time derivative α (0 < α ≤ 1). The DHAM contains the auxiliary parameter h, which provides a simple way to guarantee the convergence region of solution series. The efficiency and accuracy of the proposed method is demonstrated by test problems with initial conditions. The results obtained are compared with the exact solutions when α = 1. It is shown they are in good agreement with each other.