Table of Contents
International Scholarly Research Notices
Volume 2014, Article ID 907432, 5 pages
http://dx.doi.org/10.1155/2014/907432
Research Article

Fractional Calculus of the Generalized Mittag-Leffler Type Function

1Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur 342005, India
2Department of Mathematics, National Institute of Technology Jamshedpur, Jharkhand 831014, India

Received 22 March 2014; Accepted 6 May 2014; Published 18 August 2014

Academic Editor: Paolo Maria Mariano

Copyright © 2014 Dinesh Kumar and Sunil Kumar. 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 introduce and study a new function called -function, which is an extension of the generalized Mittag-Leffler function. We derive the relations that exist between the -function and Saigo fractional calculus operators. Some results derived by Samko et al. (1993), Kilbas (2005), Kilbas and Saigo (1995), and Sharma and Jain (2009) are special cases of the main results derived in this paper.