New analytic solutions of some fourth-order nonlinear space-time fractional partial differential equations by G' / G -expansion method

Abstract

The exact traveling wave solutions of the space-time fractional Estevez-Mansfield-Clarkson (EMC) equation and the space-time fractional Ablowitz-Kaup-Newell-Segur (AKNS) water equation are investigated. Transforming the space-time fractional EMC and the space-time fractional AKNS water equations by the Jumarie's Riemann-Liouville derivative, nonlinear ordinary differential equations (ODEs) are achived. It is observed that the G' / G -expansion method is valid and reliable for solving some nonlinear fractional PDEs. Applying the G' / G -expansion method, the solutions of EMC and AKNS water equations are obtained in terms of hyperbolic functions, trigonometric functions and rational functions.

Keywords

• g g / -expansion method
• fractional partial differential equations
• fractional estevez-mansfield-clarkson equation
• fractional ablowitz-kaup-newell-segur water equation
• analytic solution