Homotopy Perturbation Method Applied to Fractional-order Nonlinear Partial Differential Equations

Abstract

In this paper, we propose a numerical method for solving nonlinear fractional partial differential equations with fractional time derivatives. The fractional derivative is described in the Caputo sense. This method is based on the homotopy perturbation method. 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, and robotics.