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


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ÖZKAN E. M. , ÖZKAN A.

AXIOMS, vol.10, no.3, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.3390/axioms10030203
  • Journal Name: AXIOMS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Keywords: He's semi inverse method, ansatz method, beta derivative, TRAVELING-WAVE SOLUTIONS, 1ST INTEGRAL METHOD, (G'/G)-EXPANSION METHOD, GORDON EQUATIONS, SYSTEM, KDV, EVOLUTION, BRIGHT, MKDV

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, He's semi-inverse variation method 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 Atangana's conformable derivative (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.