Abstract

Fractional order Nonlinear Evolution Equations (FNLEEs) concerning to conformable fractional derivative bears great importance in various fields of real world as the model to describe underling mechanisms of nature. In this paper, we make known a new technique, called the modified fractional generalized (G'/G²)  -expansion method, to study the nonlinear space-time fractional mKdV equation and the nonlinear space-time fractional SRLW equation. A compound wave variable transformation reduces the considered equations to ordinary differential equations. Then the proposed method is employed to construct their solutions. The obtained solutions in terms of trigonometric function, hyperbolic function and rational function are claimed to be fresh and further general in closed form. These solutions might play important roles to depict the complex physical phenomena arise in nature. The modified fractional generalized (G'/G²) -expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs.

Keywords: The modified fractional generalized (G'/G²)-expansion method; compound wave variable transformation, Conformable fractional derivative, Closed form solution, Fractional order nonlinear evolution equation