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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 947986, 8 pages
http://dx.doi.org/10.1155/2013/947986
Research Article

The Time-Fractional Coupled-Korteweg-de-Vries Equations

1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
2Department of Mathematical Engineering, Yildiz Technical University, Davutpasa, 34210 Istanbul, Turkey

Received 5 January 2013; Accepted 7 February 2013

Academic Editor: Mustafa Bayram

Copyright © 2013 Abdon Atangana and Aydin Secer. 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

We put into practice a relatively new analytical technique, the homotopy decomposition method, for solving the nonlinear fractional coupled-Korteweg-de-Vries equations. Numerical solutions are given, and some properties exhibit reasonable dependence on the fractional-order derivatives’ values. The fractional derivatives are described in the Caputo sense. The reliability of HDM and the reduction in computations give HDM a wider applicability. In addition, the calculations involved in HDM are very simple and straightforward. It is demonstrated that HDM is a powerful and efficient tool for FPDEs. It was also demonstrated that HDM is more efficient than the adomian decomposition method (ADM), variational iteration method (VIM), homotopy analysis method (HAM), and homotopy perturbation method (HPM).