Moving Finite Element Methods for a System of Semi-Linear Fractional Diffusion Equations (Advances in Applied Mathematics and Mechanics, 2021)
This paper studies a system of semi-linear fractional diffusion equationswhich arise in competitive predator-prey models by replacing the second-order derivativesin the spatial variables with fractional derivatives of order less than two. Movingfinite element methods are proposed to solve the system of fractional diffusion equationsand the convergence rates of the methods are proved. Numerical examples arecarried out to confirm the theoretical findings. Some applications in anomalous diffusiveLotka-Volterra and Michaelis-Menten-Holling predator-prey models are studied.