Investigation of partial differential equations with fractional order by kudryashov method

In this study, the generalized Kudryashov method is examined which enables to obtain the exact solutions of fractional order differential equations containing the Atangana derivative. This method is a generalization of the classical Kudryashov method. This generalized method allows finding exact solutions of nonlinear differential equations involving Atangana derivative, which is a fractional derivative. This method is applied to the symmetrically regulated long wave equation containing the Atangana derivative and the modified Benjamin-Bona-Mahony equation, respectively. Different exact solutions of these equations that are not available in the literature have been obtained. In addition, three-dimensional graphs are drawn to show the physical behavior of these new exact solutions.