Application of G′G2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{G'}{G^2}$$\end{document}-Expansion Method for Solving Fractional Differential Equations

In this paper, we apply a fractional G′G2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{G'}{G^2}$$\end{document}-expansion method to look exact solutions of nonlinear fractional differential equations. A fractional complex transformation is used to convert a nonlinear FDE with Jumarie modified Riemann–Liouville derivative into its ordinary differential equation. This method is applied to two nonlinear FDEs namely, the time fractional Bogoyavlenskii equation and the space-time fractional Kundu–Eckhaus equation. It is shown that the considered method is very powerful and efficient to solve many nonlinear FDEs.