The two variable (<em>φ</em>'/<em>φ</em>, 1/<em>φ</em>)-expansion method for solving the time-fractional partial differential equations

Abstract

In this paper, we apply the two variable (φ'/φ, 1/φ)-expansion method to seek exact traveling wave solutions (solitary wave solutions, periodic function solutions, rational function solution) for time-fractional Kuramoto-Sivashinsky (K-S) equation, (3+1)-dimensional time-fractional KdV-Zakharov-Kuznetsov (KdV-ZK) equation and time-fractional Sharma-Tasso-Olver (FSTO) equation. The solutions are obtained in the form of hyperbolic, trigonometric and rational functions containing parameters. The results show that the two variable (φ'/φ, 1/φ)-expansion method is simple, effctivet, straightforward and is the generalization of the (G'/G)-expansion method.

Keywords

• the two variable (<i>φ</i>'/<i>φ</i>
• 1/<i>φ</i>)-expansion method
• nonlinear fractional differential equation
• traveling wave solution