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Abstract and Applied Analysis
Volume 2014, Article ID 498381, 7 pages
Research Article

A Modified Groundwater Flow Model Using the Space Time Riemann-Liouville Fractional Derivatives Approximation

1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
2Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa

Received 16 December 2013; Accepted 10 February 2014; Published 8 May 2014

Academic Editor: Dumitru Baleanu

Copyright © 2014 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.


The notion of uncertainty in groundwater hydrology is of great importance as it is known to result in misleading output when neglected or not properly accounted for. In this paper we examine this effect in groundwater flow models. To achieve this, we first introduce the uncertainties functions as function of time and space. The function accounts for the lack of knowledge or variability of the geological formations in which flow occur (aquifer) in time and space. We next make use of Riemann-Liouville fractional derivatives that were introduced by Kobelev and Romano in 2000 and its approximation to modify the standard version of groundwater flow equation. Some properties of the modified Riemann-Liouville fractional derivative approximation are presented. The classical model for groundwater flow, in the case of density-independent flow in a uniform homogeneous aquifer is reformulated by replacing the classical derivative by the Riemann-Liouville fractional derivatives approximations. The modified equation is solved via the technique of green function and the variational iteration method.