Abstract and Applied Analysis
Volume 2013 (2013), Article ID 934060, 8 pages
http://dx.doi.org/10.1155/2013/934060
Research Article

Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using Sumudu Transform

Jagdev Singh,1 Devendra Kumar,2 and A. Kılıçman3

1Department of Mathematics, Jagannath University, Rampura, Chaksu, Jaipur, Rajasthan 303901, India
2Department of Mathematics, Jagannath Gupta Institute of Engineering & Technology, Jaipur, Rajasthan 302022, India
3Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia

Received 12 September 2012; Revised 19 November 2012; Accepted 6 December 2012

Academic Editor: Lan Xu

Copyright © 2013 Jagdev Singh 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.

Abstract

A user friendly algorithm based on new homotopy perturbation Sumudu transform method (HPSTM) is proposed to solve nonlinear fractional gas dynamics equation. The fractional derivative is considered in the Caputo sense. Further, the same problem is solved by Adomian decomposition method (ADM). The results obtained by the two methods are in agreement and hence this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. The HPSTM is a combined form of Sumudu transform, homotopy perturbation method, and He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The numerical solutions obtained by the proposed method show that the approach is easy to implement and computationally very attractive.