Numerical solution of fractional partial differential equations by numerical Laplace inversion technique

Abstract

In this paper, we propose a numerical method for solving fractional partial differential equations. This method is based on the homotopy perturbation method and Laplace transform. The transformed problem obtained by means of temporal Laplace transform is solved by the homotopy perturbation method. Then we use Stehfest's numerical algorithm for calculating inverse Laplace transform to retrieve the time domain solution. The approximate solutions obtained by our proposed method are in excellent agreement with the exact solutions. It is worthwhile to note that our method is applicable to a variety of fractional partial differential equations occurring in fluid mechanics, signal processing, system identification, control robotics, etc. The utility of the method is shown by solving some interesting examples.