A New Version of the Generalized F-Expansion Method for the Fractional Biswas-Arshed Equation and Boussinesq Equation with the Beta-Derivative

Abstract

In this article, a new version of the generalized F-expansion method is proposed enabling to obtain the exact solutions of the Biswas-Arshed equation and Boussinesq equation defined by Atangana’s beta-derivative. First, the new version generalized F-expansion method is introduced, and then, the exact solutions of the nonlinear fractional differential equations expressed with Atangana’s beta-derivative are given. When the results are examined, it is seen that single, combined, and mixed Jacobi elliptic function solutions are obtained. From the point of view, it is understood that the new version generalized F-expansion method can give significant results in finding the exact solutions of equations containing beta-derivatives.