New wave form solutions of time-fractional Gardner equation via fractional Riccati expansion method

Abstract

In this current paper, the fractional Riccati expansion method is proposed for obtaining the new exact solutions of the time-fractional Gardner equation. The fractional derivative is considered in the sense of Jumarie’s modified Riemann-Liouville fractional derivative (JMRFD). A travelling wave transformation is firstly utilized to convert the nonlinear fractional partial differential equation (NFPDE) into a fractional ordinary differential equation (FODE). Our main intention in this present paper is to indicate that the suggested method is appropriate to obtain the new exact solutions of fractional partial differential equations. It can be said that the main advantage of the mentioned scheme is very simple and easy to apply. As a result, all the obtained results are presented in the paper.