open access

https://hdl.handle.net/2115/96163

PROPAGATING FRONT SOLUTIONS IN A TIME-FRACTIONAL FISHER-KPP EQUATION

英語

Memory effect

2024-11-02

American Institute of Mathematical Sciences (AIMS)

Discrete and continuous dynamical systems. Series B

In this paper, we treat the Fisher-KPP equation with a Caputo-type time-fractional derivative and discuss the propagation speed of the solution. The equation is a mathematical model that describes the processes of sub-diffusion, proliferation, and saturation. We first consider a traveling wave solution in studying the propagation of the solution, but we cannot define it in the usual sense, owing to the time-fractional derivative in the equation. We therefore assume that the solution asymptotically approaches a traveling wave solution, and the asymptotic traveling wave solution is formally introduced as a potential asymptotic form of the solution. The existence and properties of the asymptotic traveling wave solution are discussed using a monotone iteration method. Finally, the behavior of the solution is analyzed by conducting numerical simulations based on the results for asymptotic traveling wave solutions.

学術雑誌論文

Accepted Manuscript

This article has been published in a revised form in Discrete and continuous dynamical systems. Series B https://doi.org/10.3934/dcdsb.2024173. This version is free to download for private research and study only. Not for redistribution, re-sale or use in derivative works.

1531-3492