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

Autor: Khalid K. Ali, Asim Zafar, Waseem Razzaq, Hijaz Ahmad, Fuad A. Awwad, Emad A.A. Ismail
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Results in Physics, Vol 58, Iss , Pp 107423- (2024)
Druh dokumentu: article
ISSN: 2211-3797
DOI: 10.1016/j.rinp.2024.107423
Popis: 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.
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