The kink solitary wave and numerical solutions for conformable non-linear space–time fractional differential equations

Abstract

This paper is about the conformable non-linear space–time fractional Telegraph and the non-linear space–time fractional Kolmogorov–Petrovskii–Piskunov (KPP) equations. To construct some real and analytical wave solutions of both equations the simplest equation method is applied. As a consequence, a series of analytical wave solutions are obtained as well as verify these solutions by using Mathematica software. These solutions denote that this method is useful and straightforward. We show some graphs in 2-D and 3-D of our solution to illustrate the behaviour of waves. Finally, we introduce the numerical solutions for the conformable non-linear space–time fractional Telegraph and the non-linear space–time fractional KPP equations using the finite difference method and make comparisons with analytical solutions.

Keywords

• Fractional differential equations
• The simplest equation method
• Conformable fractional derivatives
• Travelling wave transformation
• Analytical wave solutions
• Finite difference method