Journal of Applied Mathematics
Volume 2010 (2010), Article ID 154189, 9 pages
doi:10.1155/2010/154189
Research Article

A Note on Fractional Sumudu Transform

V. G. Gupta,1 Bhavna Shrama,2 and Adem Kiliçman3

1Department of Mathematics, University of Rajasthan, Jaipur 302055, India
2Department of Mathematics, Shri Balaji Institute of Engineering and Technology, Jaipur 302045, India
3Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, (UPM), Serdang, Selangor 43400, Malaysia

Received 13 January 2010; Revised 25 March 2010; Accepted 21 April 2010

Academic Editor: Bernard Geurts

Copyright © 2010 V. G. Gupta 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

We propose a new definition of a fractional-order Sumudu transform for fractional differentiable functions. In the development of the definition we use fractional analysis based on the modified Riemann-Liouville derivative that we name the fractional Sumudu transform. We also established a relationship between fractional Laplace and Sumudu duality with complex inversion formula for fractional Sumudu transform and apply new definition to solve fractional differential equations.