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Mathematical Problems in Engineering
Volume 2014, Article ID 542809, 9 pages
Research Article

On the Generalized Mass Transport Equation to the Concept of Variable Fractional Derivative

1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
2Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 11 September 2013; Accepted 23 January 2014; Published 5 March 2014

Academic Editor: Necdet Bildik

Copyright © 2014 Abdon Atangana and Adem Kilicman. 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 hydrodynamic dispersion equation was generalized using the concept of variational order derivative. The modified equation was numerically solved via the Crank-Nicholson scheme. The stability and convergence of the scheme in this case were presented. The numerical simulations showed that, the modified equation is more reliable in predicting the movement of pollution in the deformable aquifers, than the constant fractional and integer derivatives.