An efficient computational approach for the solution of time-space fractional diffusion equation

Abstract

The main aim of this paper is to construct an efficient recursive algorithm to solve a time-space fractional Poisson’s equation which can be treated as a time-space fractional diffusion equation in two dimensions. The fractional derivatives in both time and space are defined in the Caputo sense. A homotopy perturbation method is introduced to approximate the solution, and a comparison is made between the exact and the approximate solutions. In addition, we present a procedure for solving higher-order fractional Poisson’s equations. In this case, the equation is converted to a system of fractional differential equations in which the order of the time derivatives is less than or equal to one. The convergence analysis is carried out, and an apriori bound of the solution is obtained for the present problem. Numerical examples are provided and the experimental evidence proves the effectiveness of the proposed method.