Fractional Reaction-Diffusion Equations for Modelling Complex Biological Patterns

Ku Azlina Ku Akil, Sithi V Muniandy, Einly Lim

Abstract


We consider a system of nonlinear time-fractional reaction-diffusion equations (TFRDE) on a finite spatial domain x ∈ [0, L], and time t ∈ [0, T]. The system of standard reaction-diffusion equations with Neumann boundary conditions are generalized by replacing the first-order time derivatives with Caputo time-fractional derivatives of order α ∈ (0, 1). We solve the TFRDE numerically using Grünwald-Letnikov derivative approximation for time-fractional derivative and centred difference approximation for spatial derivative. We discuss the numerical results and propose the applications of TFRDE for the modelling of complex patterns in biological systems.

Keywords


Fractional reaction-diffusion; Fractional derivative; Caputo derivative; Grünwald-Letnikov derivative;

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DOI: https://doi.org/10.11113/mjfas.v8n3.135

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