Abstract

GUREFE, Yusuf. The generalized Kudryashov method for the nonlinear fractional partial differential equations with the beta-derivative. Rev. mex. fis. [online]. 2020, vol.66, n.6, pp.771-781.  Epub Jan 31, 2022. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.66.771.

In this article, we consider the exact solutions of the Hunter-Saxton and Schrödinger 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.

Keywords : The generalized Kudryashov method; Hunter-Saxton equation; Schrödinger equation; beta-derivative; wave solutions.