Eur. Phys. J. Plus (2018) 133: 45
https://doi.org/10.1140/epjp/i2018-11896-0

Regular Article

A new modification in the exponential rational function method for nonlinear fractional differential equations

¹ Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt, Pakistan
² Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan
³ Center for Research (CFR), University of Islamabad (UoI), Islamabad, Pakistan

^* e-mail: umarkhan@ciit.net.pk

Received: 20 October 2017
Accepted: 10 January 2018
Published online: 12 February 2018

Abstract

We have modified the traditional exponential rational function method (ERFM) and have used it to find the exact solutions of two different fractional partial differential equations, one is the time fractional Boussinesq equation and the other is the (2+1)-dimensional time fractional Zoomeron equation. In both the cases it is observed that the modified scheme provides more types of solutions than the traditional one. Moreover, a comparison of the recent solutions is made with some already existing solutions. We can confidently conclude that the modified scheme works better and provides more types of solutions with almost similar computational cost. Our generalized solutions include periodic, soliton-like, singular soliton and kink solutions. A graphical simulation of all types of solutions is provided and the correctness of the solution is verified by direct substitution. The extended version of the solutions is expected to provide more flexibility to scientists working in the relevant field to test their simulation data.