Anomalous Diffusion and Analytical Approximate Solution of Fractional Diffusion Equation

摘要

Anomalous diffusion happens often in nature and society systems. In this paper, we develop a non-local method with temporal and spatial correlations to introduce a fractional order advection-diffusion equation based on the usually used local 2- nd order advection-dispersion equation. In this paper, a kind of time-space (two dimension) fractional-order anomalous diffusion equation is considered ,and an approximate solution is constructed by using Adomian decomposition method. Further we showed one example to compare the error of exact solution and approximate solution, which illustrated that the method is efficiency for this kind fractional-order anomalous diffusion equation.