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Advances in Mathematical Physics
Volume 2015 (2015), Article ID 746327, 8 pages
Research Article

On the Nonlinear Perturbation Rosenau-Hyman Equation: A Model of Nonlinear Scattering Wave

1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
2Institute of Space Sciences, P.O. Box MG-23, Măgurele, 077125 Bucharest, Romania
3Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
4Mathematics Department, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia
5Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou, Jiangsu 221008, China

Received 18 May 2015; Accepted 4 November 2015

Academic Editor: Fawang Liu

Copyright © 2015 Abdon Atangana et al. 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.


We investigate a nonlinear wave phenomenon described by the perturbation Rosenau-Hyman equation within the concept of derivative with fractional order. We used the Caputo fractional derivative and we proposed an iteration method in order to find a particular solution of the extended perturbation equation. We proved the stability and the convergence of the suggested method for solving the extended equation without any restriction on and also on the perturbations terms. Using the inner product we proved the uniqueness of the special solution. By choosing randomly the fractional orders and , we presented the numerical solutions.