A numerical method for solving the time variable fractional order mobile-immobile advection-dispersion model

In this article, we proposed a new numerical method to obtain the approximation solution for the time variable fractional order mobile-immobile advection-dispersion model based on reproducing kernel theory and collocation method. The equation is obtained from the standard advection-dispersion equation (ADE) by adding the Coimbra's variable fractional derivative in time of order gamma (x, t) is an element of [0, 1]. In order to solve this kind of equation, we discuss and derive the epsilon-approximate solution in the form of series with easily computable terms in the bivariate spline space. At the same time, the stability and convergence of the approximation are investigated. Finally, numerical examples are provided to show the accuracy and effectiveness. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.