Abstract and Applied Analysis
Volume 2013 (2013), Article ID 608943, 8 pages
http://dx.doi.org/10.1155/2013/608943
Research Article

An Efficient Approach for Fractional Harry Dym Equation by Using Sumudu Transform

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

1Department of Mathematics, JaganNath Gupta Institute of Engineering and Technology, Jaipur, Rajasthan 302022, India
2Department of Mathematics, JaganNath University, Village-Rampura, Tehsil-Chaksu, Jaipur, Rajasthan 303901, India
3Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 13 March 2013; Accepted 22 April 2013

Academic Editor: Mustafa Bayram

Copyright © 2013 Devendra Kumar 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

An efficient approach based on homotopy perturbation method by using sumudu transform is proposed to solve nonlinear fractional Harry Dym equation. This method is called homotopy perturbation sumudu transform (HPSTM). Furthermore, 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 HPSTM show that the approach is easy to implement and computationally very attractive.