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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 546062, 11 pages
http://dx.doi.org/10.1155/2012/546062
Research Article

A Generalized q-Mittag-Leffler Function by q-Captuo Fractional Linear Equations

Department of Mathematics and Computer Science, Çankaya University, 06530 Ankara, Turkey

Received 23 January 2012; Accepted 20 February 2012

Academic Editor: Juan J. Trujillo

Copyright © 2012 Thabet Abdeljawad 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

Some Caputo q-fractional difference equations are solved. The solutions are expressed by means of a new introduced generalized type of q-Mittag-Leffler functions. The method of successive approximation is used to obtain the solutions. The obtained q-version of Mittag-Leffler function is thought as the q-analogue of the one introduced previously by Kilbas and Saigo (1995).