  In this paper, we develop a numerical resolution of the space-time fractional
advection-dispersion equation. After time discretization, we utilize
collocation technique and implement a product integration method in order to
simplify the evaluation of the terms involving spatial fractional order
derivatives. Then utilizing Bernstein polynomials as basis, the problem is
transformed into a linear system of algebraic equations. Error analysis and
order of convergence for the proposed method are also discussed. Some numerical
experiments are presented to demonstrate the effectiveness of the proposed
method and to confirm the analytic results.
