Fractional Calculus of the Generalized Mittag-Leffler Type Function

Abstract

We introduce and study a new function called R -function, which is an extension of the generalized Mittag-Leffler function. We derive the relations that exist between the R -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.