Approximate solution of the fractional advection-dispersion equation

In this paper, we consider practical numerical method to solve a space-time fractional advection-dispersion equation with variable coefficients on a finite domain. The equation is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative, and the first-order and second-order space derivatives by the Riemann-Liouville fractional derivative, respectively. Here, a new method for solving this equation is proposed in the reproducing kernel space. The representation of solution is given by the form of series and the n-term approximation solution is obtained by truncating the series. The method is easy to implement and the numerical results show the accuracy of the method. (C) 2009 Elsevier B.V. All rights reserved.