A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations

Shehu Maitama

doi:10.1155/2016/9207869

Abstract

A hybrid analytical method for solving linear and nonlinear fractional partial differential equations is presented. The proposed analytical approach is an elegant combination of the Natural Transform Method (NTM) and a well-known method, Homotopy Perturbation Method (HPM). In this analytical method, the fractional derivative is computed in Caputo sense and the nonlinear term is calculated using He’s polynomial. The proposed analytical method reduces the computational size and avoids round-off errors. Exact solution of linear and nonlinear fractional partial differential equations is successfully obtained using the analytical method.

Highlights

The fractional derivative is computed in Caputo sense and the nonlinear term is calculated using He’s polynomial
The concept of fractional calculus which deals with derivatives and integrals of arbitrary orders [1] plays a significant role in many areas of physical science and engineering
There is a rapid development in the concept of fractional calculus and its applications [2,3,4,5]

Summary

Introduction

The concept of fractional calculus which deals with derivatives and integrals of arbitrary orders [1] plays a significant role in many areas of physical science and engineering. The linear and nonlinear fractional differential equations are used to model significant problems in fluid mechanics, acoustic, electromagnetism, signal processing, analytical chemistry, biology, and many other areas of physical science and engineering [6]. An analytical method called a Hybrid Natural Transform Homotopy Perturbation Method for solving linear and nonlinear fractional partial differential equations is introduced. Exact solution of linear and nonlinear fractional partial differential equation is successfully obtained using the new analytical method. The Hybrid Natural Transform Homotopy Perturbation Method is a powerful mathematical method for solving linear and nonlinear fractional partial differential equations and is a refinement of the existing methods

Natural Transform

Basic Definitions of Fractional Calculus

Analysis of the Method

Applications

Conclusion