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Mathematical Problems in Engineering
Volume 2013, Article ID 318590, 9 pages
Research Article

Solving Partial Differential Equation with Space- and Time-Fractional Derivatives via Homotopy Decomposition Method

1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
2Department of Mathematics and Computer Science, College of Science, Alfaisal University, P.O. Box 50927, Riyadh 11533, Saudi Arabia

Received 17 September 2013; Accepted 9 October 2013

Academic Editor: Muhammet Kurulay

Copyright © 2013 Abdon Atangana and Samir Brahim Belhaouari. 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 analytical solution of the partial differential equation with time- and space-fractional derivatives was derived by means of the homotopy decomposition method (HDM). Some examples are given and comparisons are made. The evaluations show that the homotopy decomposition method is extremely successful and suitable. The achieved results make the steadfastness of the HDM and its wider applicability to fractional differential equation obvious. Additionally, the adding up implicated in HDM is exceptionally undemanding and uncomplicated. It is confirmed that HDM is an influential and professional apparatus for FPDEs. It was also established that HDM is supplementary well organized than the ADM, VIM, HAM, and HPM.