The generalized Kudryashov method for the nonlinear fractional partial differential equations with the beta-derivative

Gurefe Y.

Revista Mexicana de Fisica, vol.66, no.6, pp.771-781, 2020 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 66 Issue: 6
  • Publication Date: 2020
  • Doi Number: 10.31349/revmexfis.66.771
  • Journal Name: Revista Mexicana de Fisica
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, DIALNET
  • Page Numbers: pp.771-781
  • Keywords: beta-derivative, Hunter-Saxton equation, Schr¨odinger equation, The generalized Kudryashov method, wave solutions
  • Uşak University Affiliated: Yes

Abstract

In this article, we consider the exact solutions of the Hunter-Saxton and Schr¨odinger equations defined by Atangana’s conformable derivative using the general Kudryashov method. Firstly, Atangana’s conformable fractional derivative and its properties are included. Then, by introducing the generalized Kudryashov method, exact solutions of nonlinear fractional partial differential equations, which can be expressed with the conformable derivative of Atangana, are classified. Looking at the results obtained, it is understood that the generalized Kudryashov method can yield important results in obtaining the exact solutions of fractional partial differential equations containing beta-derivatives.