(8)Traveling wave solutions to some nonlinear fractional partial differential equations through the rational (G′/G)-expansion method

Tarikul Islam a , M. Ali Akbar b , ∗, Abul Kalam Azad b
a Department of Mathematics, Hajee Mohammad Danesh Science and Technology University, Dinajpur, Bangladesh

b Department of Applied Mathematics, Rajshahi University, Rajshahi, Bangladesh

Received 10 November 2017; received in revised form 23 December 2017; accepted 29 December 2017
Available online 5 January 2018

Abstract
In this article, the analytical solutions to the space-time fractional foam drainage equation and the space-time fractional symmetric regularized long wave (SRLW) equation are successfully examined by the recently established rational ( G  / G )-expansion method. The suggested equations are reduced into the nonlinear ordinary differential equations with the aid of the fractional complex transform. Consequently, the theories of the ordinary differential equations are implemented effectively. Three types closed form traveling wave solutions, such as hyper- bolic function, trigonometric function and rational, are constructed by using the suggested method in the sense of conformable fractional derivative. The obtained solutions might be significant to analyze the depth and spacing of parallel subsurface drain and small-amplitude long wave on the surface of the water in a channel. It is observed that the performance of the rational ( G  / G )-expansion method is reliable and will be used to establish new general closed form solutions for any other NPDEs of fractional order.
© 2018 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Keywords: Nonlinear space-time fractional equations; Nonlinear fractional complex transformation; Conformable fractional derivative; Exact solutions.