Exact solutions for fractional partial differential equations by a new fractional sub-equation method

Abstract

In this paper, we propose a new fractional sub-equation method for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative, which is the fractional version of the known (G /G) method. To illustrate the validity of this method, we apply it to the space-time fractional Fokas equation, the space-time fractional (2 + 1)-dimensional dispersive long wave equations and the space-time fractional fifth-order Sawada-Kotera equation. As a result, some new exact solutions for them are successfully established. MSC: 35Q51; 35Q53

A new method for solving nonlinear fractional differential equations

“…In literature, exact solutions of fractional differential equations have attracted the attention of researcher from different fields. Several research works have proposed techniques for solving fractional differential equations, such as G ′ /G−expansion method [3,28,30] , Exp−function method [12,29], first integral method [1,8,19,22], sub−equation method [13,24,32], Jacobi elliptic funtion method [9,11,26,31] , modified Kudryashov method [4,5,6,17,20], extended tanh method [7],modified simple equation method [18] and others.…”

“…Moreover, traveling wave solutions of these equations have been studied in [10,21,26,30,28,32], the symmetrical Fibonacci function solutions and hyperbolic function solutions have been obtained by classical Kudryashov method in [6].…”

Traveling Wave Solutions for the Nonlinear Fractional Sharma-Tasso-Olever Equation

“…It is too According to Set 1, and considering Eq. (9), (11), (14) at the same time, we find out the following explicit solutions to the fractional STO equation (10) …”

Exact Solutions of a Family of Higher-Dimensional Space-Time Fractional KDV-Type Equations

“…Therefore, the efficient approaches to construct the solutions of FPDEs have attracted great interest by several groups of researchers. A large collection of analytical and computational methods has been introduced for this reason, for example the exp-function method [3,4], Adomian decomposition method [5], the ( / ) G G ′ -expansion method [6], the first integral method [7,8], the variational iteration method [9], the subequation method [10,11], the modified simple equation method [12], Jacobi elliptic function expansion method [13], the generalized Kudryashov method [14,15] and so on. One of the most powerful methods for seeking analytical solutions of nonlinear differential equations is the functional variable method, which was first proposed by Zerarka et al [16,17] in 2010.…”