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arXiv · 2507.02094

Tools for stability analysis of fractional reaction diffusion systems

Sofwah Ahmad·Szymon Cygan·Grzegorz Karch
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Abstract

The linearization principle states that the stability (or instability) of solutions to a suitable linearization of a nonlinear problem implies the stability (or instability) of solutions to the original nonlinear problem. In this work, we prove this principle for solutions of abstract fractional reaction-diffusion equations with a fractional derivative in time of order $\alpha\in (0,1)$. Then, we apply these results to particular fractional reaction-diffusion equations, obtaining, for example, the counterpart of the classical Turing instability in the case of fractional equations.

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Sofwah Ahmad, Szymon Cygan, Grzegorz Karch. 2025-07-02. Tools for stability analysis of fractional reaction diffusion systems. https://arxiv.org/abs/2507.02094

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