Some new exact solutions to fractional potential Korteweg-de Vries equation

Abstract

The objective of this paper is to find the exact soliton solutions to a nonlinear fractional partial differential equation (known as fractional potential Korteweg-de Vries (fp-KdV) equation). We have made use of complex wave transformation with Jumarie's Riemann-Liouville (R-L) derivative to convert fp-KdV into corresponding fractional ODE. This process is a part of fractional sub-equation method (FSEM) that we have implemented to solve the equation at hand. Using this method, we have obtained five different types of exact soliton solutions i.e. trigonometric, hyperbolic and rational. These solutions are novel and would help us to have a deeper understanding of the phenomenon governed by fp-KdV equation.