Closed form traveling wave solutions of non-linear fractional evolution equations through the modified simple equation method

Abstract

In this article, the modified simple equation (MSE) method is introduced to examine the closed form wave solutions of the fractional non-linear Cahn-Allen equation and of the fractional generalized reaction Duffing equation. The fractional derivatives are delineated in the sense of Jumarie?s modified Riemann-Liouville derivative. A fractional complex transformation is used to transform the fractional-order PDE into integer order ODE. The reduced equations are then examined by using the MSE method and some new and further general solutions of these equations are successfully established. The approach of this method is simple, standard and the obtained solutions are highly encouraging. It is also powerful, reliable and effective.