The Soliton Solutions for Some Nonlinear Fractional Differential Equations with Beta Derivative

TL;DR

This paper applies semi inverse variation and ansatz methods to find soliton solutions for fractional nonlinear equations with Beta derivative, confirmed through Maple computations and graphical analysis, advancing solutions in mathematical physics.

Contribution

It introduces effective methods for solving fractional nonlinear equations with Beta derivative, providing explicit soliton solutions confirmed by computational and graphical methods.

Findings

Successfully derived soliton solutions for fractional KdV, equal width, and modified equal width equations.

Validated solutions through Maple calculations and graphical representations.

Demonstrated potential applications in mathematical physics and engineering.

Abstract

Nonlinear fractional differential equations have gained a significant place in mathematical physics. Finding the solutions to these equations has emerged as a field of study that has attracted a lot of attention lately. In this work, semi inverse variation method of He and the ansatz method have been applied to find the soliton solutions for fractional Korteweg de Vries equation, fractional equal width equation, and fractional modified equal width equation defined by conformable derivative of Atangana (beta derivative). These two methods are effective methods employed to get the soliton solutions of these nonlinear equations. All of the calculations in this work have been obtained using the Maple program and the solutions have been replaced in the equations and their accuracy has been confirmed. In addition, graphics of some of the solutions are also included. The found solutions in this study have the potential to be useful in mathematical physics and engineering.