Solitary wave solutions to some nonlinear conformable partial differential equations

Fractional calculus is a field that is currently used in the world’s applications in many science and engineering fields where many models are still being developed and researched. The conformable time-fractional gives the full history of this function, which is the advantage of using fractional calculus to solve physical problems. In this study, the conformable time-fractional extended (2  1)-dimensional quantum Zakharov-Kuznetsov and the time-fractional modified Korteweg-de Vries equations are investigated by using the the modified exp (−Ω(ξ))-expansion function approach. Some new prototype analytical solutions such the hyperbolic and trigonometric function solutions are successfully reached. The importance of current research is to derive new solutions using a strong analytical approach. All the reported solutions in this study have verified their corresponding model. Under the choice of suitable values of the parameters involved, the 3D and 2D to the obtained solutions are successfully plotted.

Keyword: conformable derivative; hyperbolic function; the MEFM; trigonometric function