An efficient technique for solving linear and nonlinear fractional partial differential equations

Abstract

This paper introduces an analytical method called the Natural Homotopy Perturbation Method (NHPM) for solving linear and nonlinear fractional partial differential equations. The analytical method is a coupling of the Natural Transform Method (NTM) and a well-known technique, Homotopy Perturbation Method (HPM). The proposed analytical method gives a series solution which converges rapidly within few iterations, and it reduces the computational size and avoids round-off errors.  The fractional derivative are computed in Caputo sense, and the nonlinear terms are computed using He's polynomials. The efficiency, simplicity and high accuracy of the proposed analytical method are clearly illustrated.