Abstract and Applied Analysis
Volume 2013 (2013), Article ID 691060, 8 pages
http://dx.doi.org/10.1155/2013/691060
Research Article

Stability and Convergence of a Time-Fractional Variable Order Hantush Equation for a Deformable Aquifer

Abdon Atangana1 and S. C. Oukouomi Noutchie2

1Institute for Groundwater Studies, University of the Free State, P.O. Box 399, Bloemfontein, South Africa
2Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa

Received 21 March 2013; Revised 30 April 2013; Accepted 7 May 2013

Academic Editor: Bashir Ahmad

Copyright © 2013 Abdon Atangana and S. C. Oukouomi Noutchie. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The medium through which the groundwater moves varies in time and space. The Hantush equation describes the movement of groundwater through a leaky aquifer. To include explicitly the deformation of the leaky aquifer into the mathematical formulation, we modify the equation by replacing the partial derivative with respect to time by the time-fractional variable order derivative. The modified equation is solved numerically via the Crank-Nicolson scheme. The stability and the convergence in this case are presented in details.