Soliton Solutions of Fractional order KdV-Burger's Equation

TL;DR

This paper derives exact traveling wave solutions for the fractional KdV-Burgers equation using fractional complex transformation and the (G'/G)-expansion method, advancing analytical methods for fractional nonlinear PDEs.

Contribution

It introduces a novel combination of fractional complex transformation and the (G'/G)-expansion method to find soliton solutions of the fractional KdV-Burgers equation.

Findings

Exact traveling wave solutions obtained.

Method applicable to other fractional nonlinear equations.

Enhanced understanding of fractional soliton dynamics.

Abstract

In this article, the new exact travelling wave solutions of the time-and space-fractional KdV-Burgers equation has been found. For this the fractional complex transformation have been implemented to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations, in the sense of the Jumarie's modified Riemann-Liouville derivative. Afterwards, the improved (G'/G)-expansion method can be implemented to celebrate the soliton solutions of KdV-Burger's equation of fractional order.