Tools for stability analysis of fractional reaction diffusion systems

2025/07/02 by Ahmad, Sofwah, Cygan, Szymon, Karch, Grzegorz
#34G20 #35B35 #35B40 #35K57 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.02094

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 α∈ (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.

Citations

• Abstract Differential Equations and Caputo Fractional Derivative
• Stability of constant steady states of a chemotaxis model
• The chemical basis of morphogenesis

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