Similarities in a fifth-order evolution equation with and with no singular kernel

By Emile-Franc Doungmo Goufo, Sunil Kumar, S. Mugisha. 2020

196 citations recorded by the source corpus.

Abstract We perform in this report a comparative analysis between differential fractional operators applied to the non-linear Kaup–Kupershmidt equation. Such operators include the Atangana–Beleanu derivative and the Caputo–Fabrizio derivative which respectively follow the Mittag-Leffler law and the exponential law. We exploit the fixed points of the dynamics and the stability analysis to demonstrate that the exact solution exists and is unique for both types of models. Methods of performing numerical approximations of the solutions are presented and illustrated by graphical representations exhibiting a clear comparison between the dynamics under the influence of Mittag-Leffler law and those under the exponential law. Different cases are presented with respect to values of the derivative order 0  α = 1 ).

Subfields: Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/55386c78fd7d54c261abc588dc6542c2962e01f5