Solving Some Important Nonlinear Time-Fractional Evolution Equations by Using the (G’/G)-Expansion Method

Abstract

The aim of the present study is to find the exact solutions for three generalized nonlinear time-fractional evolution equations, Kaup-Kupershmidt equation, Burgers-Fisher equation and, Shallow Water Wave equation. By using the (G’/G)-expansion method and depending on second order linear ODE as well as the complex transformation, three kinds of solutions (hyperbolic, trigonometric, and rational) are obtained. With the help of Mathematica software package, difficult algebraic systems are solved and surfaces of some particular solutions of the equations under study are plotted.

Various new traveling wave solutions for conformable time-fractional Sasa-Satsuma equation

“…In literature, to investigate the exact solutions for fractional PDEs, the authors use many forms of fractional derivative, in particular, Riemann Liouville, Jumarie's modified Riemann-Liouville and Caputo derivatives [2,5,6,7,8,16,23].…”