Eur. Phys. J. Plus (2017) 132: 319
https://doi.org/10.1140/epjp/i2017-11590-9

Regular Article

Exact solution of the space-time fractional coupled EW and coupled MEW equations

¹ Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt
² Mathematics Department, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt

^* e-mail: khalidkaram2012@yahoo.com

Received: 10 April 2017
Accepted: 9 June 2017
Published online: 21 July 2017

Abstract

In this paper, we obtained a traveling wave solution by using the Kudryashov method for the space-time fractional nonlinear partial differential equations. The method is used to obtain the exact solutions for different types of the space-time fractional nonlinear partial differential equations, such as the space-time fractional coupled equal width wave equation (CEWE) and the space-time fractional coupled modified equal width wave equation (CMEWE), which are the important soliton equations. Both equations are reduced to ordinary differential equations by use of the fractional complex transform and of the properties of the modified Riemann-Liouville derivative. We plot the exact solutions for these equations at different time levels.