The G′G-expansion method using modified Riemann–Liouville derivative for some space-time fractional differential equations

Abstract

In this paper, the fractional partial differential equations are defined by modified Riemann–Liouville fractional derivative. With the help of fractional derivative and traveling wave transformation, these equations can be converted into the nonlinear nonfractional ordinary differential equations. Then G′G-expansion method is applied to obtain exact solutions of the space-time fractional Burgers equation, the space-time fractional KdV-Burgers equation and the space-time fractional coupled Burgers’ equations. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. These results reveal that the proposed method is very effective and simple in performing a solution to the fractional partial differential equation.

Keywords

• The G′G-expansion method
• The space-time fractional Burgers equation
• The space-time fractional KdV-Burgers equation
• The space-time fractional coupled Burgers’ equations