An Implicit Approximation for the Caputo Fractional Reaction-Dispersion Equation

Fractional differential equations can more correctly simulate many phenomena contrasting with integer differential equations in lost of applied science.In this paper,a time-fractional reaction-dispersion equation was considered which the first order derivative was replaced by a Caputo fractional derivative,and an implicit difference scheme was given.Stability and convergence were proved by using energy method.A numerical example demonstrates the difference method is effective.