New Analytical Solutions of Conformable Time Fractional Bad and Good Modified Boussinesq Equations

Creative Commons License

Durur H., TAŞBOZAN O., Kurt A.

Applied Mathematics and Nonlinear Sciences, vol.5, no.1, pp.447-454, 2020 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.2478/amns.2020.1.00042
  • Journal Name: Applied Mathematics and Nonlinear Sciences
  • Journal Indexes: Scopus, Applied Science & Technology Source, Compendex, zbMATH, DIALNET
  • Page Numbers: pp.447-454
  • Keywords: auxiliary equation method, bad and good modified Boussinesq equations, conformable fractional derivative
  • Open Archive Collection: AVESIS Open Access Collection
  • Hatay Mustafa Kemal University Affiliated: Yes

Abstract

The main purpose of this article is to obtain the new solutions of fractional bad and good modified Boussinesq equations with the aid of auxiliary equation method, which can be considered as a model of shallow water waves. By using the conformable wave transform and chain rule, nonlinear fractional partial differential equations are converted into nonlinear ordinary differential equations. This is an important impact because both Caputo definition and Riemann-Liouville definition do not satisfy the chain rule. By using conformable fractional derivatives, reliable solutions can be achieved for conformable fractional partial differential equations.