Asymptotic dynamics of non-autonomous fractional reaction-diffusion equations on bounded domains

2020 ◽  
pp. 1
Author(s):  
Xin Li ◽  
Wenxian Shen ◽  
Chunyou Sun
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Bounded Domains ◽  
Asymptotic Dynamics ◽  
Fractional Reaction

scholarly journals Fractional Reaction-Diffusion Equations for Modelling Complex Biological Patterns

2014 ◽  
Vol 8 (3) ◽  
Author(s):  
Ku Azlina Ku Akil ◽  
Sithi V Muniandy ◽  
Einly Lim
Keyword(s):  
Fractional Derivatives ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Difference Approximation ◽  
Standard Reaction ◽  
Biological Patterns ◽  
Derivatives Of ◽  
Fractional Reaction

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.

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