  Time fractional advection-dispersion equations arise as generalizations of
classical integer order advection-dispersion equations and are increasingly
used to model fluid flow problems through porous media. In this paper we
develop an implicit finite difference method to solve a two-dimensional initial
boundary value problem for the linear time fractional advection-dispersion
equation with variable coefficients on a bounded domain. Consistency, stability
and convergence of the method are proved in detail and the numerical
experiments offer a good insight into the quality of the obtained
approximations.
