Journal of Applied Mathematics
Volume 2010 (2010), Article ID 154189, 9 pages
A Note on Fractional Sumudu Transform
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.
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.