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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 696597, 6 pages
http://dx.doi.org/10.1155/2013/696597
Research Article

A Possible Generalization of Acoustic Wave Equation Using the Concept of Perturbed Derivative Order

1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
2Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Malaysia

Received 18 February 2013; Accepted 18 March 2013

Academic Editor: Guo-Cheng Wu

Copyright © 2013 Abdon Atangana and Adem Kılıçman. 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

The standard version of acoustic wave equation is modified using the concept of the generalized Riemann-Liouville fractional order derivative. Some properties of the generalized Riemann-Liouville fractional derivative approximation are presented. Some theorems are generalized. The modified equation is approximately solved by using the variational iteration method and the Green function technique. The numerical simulation of solution of the modified equation gives a better prediction than the standard one.