Generalized exponential rational function method to the fractional shallow water wave phenomena

Abstract

In this study we introduce the fractional shallow water wave phenomena, namely, the new extended (2 + 1)-dimensional fractional Boussinesq equation and in the following we apply the generalized exponential rational function for extracting the soliton solutions to the Ex-FBe (extended (2 + 1)-dimensional fractional Boussinesq equation) by using Maple tools for calculating and Mathematica for graphical behaviors. Many types of exact soliton solutions for the fswwp equation have been derived by the erf method. Physical interpretations of some of the obtained solutions are also included. It can be easily concluded that the new proposed method is very efficient and finds the exact solutions of the equation in a relatively easy way.