A New Fractional Subequation Method and Its Applications for Space-Time Fractional Partial Differential Equations

Fanwei Meng,Qinghua Feng

doi:10.1155/2013/481729

Abstract

A new fractional subequation method is proposed for finding exact solutions for fractional partial differential equations (FPDEs). The fractional derivative is defined in the sense of modified Riemann-Liouville derivative. As applications, abundant exact solutions including solitary wave solutions as well as periodic wave solutions for the space-time fractional generalized Hirota-Satsuma coupled KdV equations are obtained by using this method.

Highlights

Fractional differential equations are generalizations of classical differential equations of integer order
Fractional differential equations have been the focus of many studies due to their frequent appearance in various applications in physics, biology, engineering, signal processing, systems identification, control theory, finance, and fractional dynamics
We propose a new fractional subequation method to establish exact solutions for fractional partial differential equations (FPDEs), which is based on the following fractional ordinary differential equation: Dξ2αG (ξ) + λDξαG (ξ) + μG (ξ) = 0, 0 < α ≤ 1, (1)

Summary

Introduction

Fractional differential equations are generalizations of classical differential equations of integer order. Some powerful methods have been proposed so far (e.g., see [1,2,3,4,5,6,7,8,9,10,11,12]) Using these methods, a variety of fractional differential equations have been investigated. We propose a new fractional subequation method to establish exact solutions for fractional partial differential equations (FPDEs), which is based on the following fractional ordinary differential equation: Dξ2αG (ξ) + λDξαG (ξ) + μG (ξ) = 0, 0 < α ≤ 1, (1).

Description of the Fractional Subequation Method

Conclusions