Fractional Reaction-Diffusion Equations for Modelling Complex Biological Patterns
DOI:
https://doi.org/10.11113/mjfas.v8n3.135Keywords:
Fractional reaction-diffusion, Fractional derivative, Caputo derivative, Grünwald-Letnikov derivative,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.References
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