Derivation and solution of space fractional modified Korteweg de Vries equation

Abstract

All applications of fractional calculus to physics propose fractional equations of motion for various complex phenomena. Complex and nonlinear fractional equations are very familiar and often occur in nature. Therefore, the analytical and numerical solutions of this kind of equations are very important and consequential. An important objective in this study is to derive the space fractional modified Korteweg de Vries (SFMKdV) equation and present an efficient modified G′/G -expansion method to solve it. The exact analytical solution of SFMKdV equation is obtained to describe the space fractional parameter effect on the propagation of the ion acoustic (IA) waves. It has been observed that space fractional parameter can modify the height of the IA waves.