Table of Contents
ISRN Mathematical Physics
Volume 2014 (2014), Article ID 217184, 11 pages
http://dx.doi.org/10.1155/2014/217184
Research Article

Assessment of the Exact Solutions of the Space and Time Fractional Benjamin-Bona-Mahony Equation via the -Expansion Method, Modified Simple Equation Method, and Liu’s Theorem

Theoretical Physics Group, Department of Physics, University of Ibadan, Ibadan, Nigeria

Received 28 November 2013; Accepted 9 January 2014; Published 6 March 2014

Academic Editors: B. Bagchi, D. Singleton, and M. Znojil

Copyright © 2014 Olusola Kolebaje and Oyebola Popoola. 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

Exact travelling wave solutions to the space and time fractional Benjamin-Bona-Mahony (BBM) equation defined in the sense of Jumarie’s modified Riemann-Liouville derivative via the expansion and the modified simple equation methods are presented in this paper. A fractional complex transformation was applied to turn the fractional BBM equation into an equivalent integer order ordinary differential equation. New complex type travelling wave solutions to the space and time fractional BBM equation were obtained with Liu’s theorem. The modified simple equation method is not effective for constructing solutions to the fractional BBM equation.