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arXiv · 2511.05312

A time-fractional Fisher-KPP equation for tumor growth: Analysis and numerical simulation

Marvin Fritz·Nikos I. Kavallaris
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Abstract

We study a time-fractional Fisher-KPP equation involving a Riemann-Liouville fractional derivative acting on the diffusion term, as derived by Angstmann and Henry (Entropy, 22:1035, 2020). The model captures memory effects in diffusive population dynamics and serves as a framework for tumor growth modeling. We first establish local well-posedness of weak solutions. The analysis combines a Galerkin approximation with a refined a priori estimate based on a Bihari-Henry-Gronwall inequality, addressing the nonlinear coupling between the fractional diffusion and the reaction term. For small initial data, we further prove global well-posedness and asymptotic stability. A numerical method based on a nonuniform convolution quadrature scheme is then proposed and validated. Simulations demonstrate distinct dynamical behaviors compared to conventional formulations, emphasizing the physical consistency of the present model in describing tumor progression.

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Marvin Fritz, Nikos I. Kavallaris. 2025-11-07. A time-fractional Fisher-KPP equation for tumor growth: Analysis and numerical simulation. https://arxiv.org/abs/2511.05312

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