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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 828764, 8 pages
http://dx.doi.org/10.1155/2013/828764
Research Article

Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes

1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
2Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia
3Department of Mathematics and Computer Sciences, Cankaya University, Faculty of Art and Sciences, Balgat, 06530 Ankara, Turkey
4Institute of Space Sciences, P.O. Box MG-23, Magurele, 76900 Bucharest, Romania

Received 5 August 2013; Accepted 23 August 2013

Academic Editor: Soheil Salahshour

Copyright © 2013 Abdon Atangana and Dumitru Baleanu. 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

A kind of parabolic equation was extended to the concept of fractional calculus. The resulting equation is, however, difficult to handle analytically. Therefore, we presented the numerical solution via the explicit and the implicit schemes. We presented together the stability and convergence of this time-fractional parabolic equation with two difference schemes. The explicit and the implicit schemes in this case are stable under some conditions.