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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 270106, 16 pages
http://dx.doi.org/10.1155/2012/270106
Research Article

On Sumudu Transform Method in Discrete Fractional Calculus

Department of Mathematics and Computer Science, Cankaya University, Eskisehir Yolu 29 km, 06810 Ankara, Turkey

Received 16 April 2012; Revised 4 June 2012; Accepted 5 June 2012

Academic Editor: Paul Eloe

Copyright © 2012 Fahd Jarad and Kenan Taş. 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

In this paper, starting from the definition of the Sumudu transform on a general time scale, we define the generalized discrete Sumudu transform and present some of its basic properties. We obtain the discrete Sumudu transform of Taylor monomials, fractional sums, and fractional differences. We apply this transform to solve some fractional difference initial value problems.