Fractional calculus of the generalized Mittag-Leffler type function (Q1727835)

Summary: 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 \textit{St. G. Samko} et al. [Fractional integrals and derivatives: theory and applications. Transl. from the Russian. New York, NY: Gordon and Breach (1993; Zbl 0818.26003)], \textit{A. A. Kilbas} [Fract. Calc. Appl. Anal. 8, No. 2, 113--126 (2005; Zbl 1144.26008)], \textit{A. A. Kilbas} and \textit{M. Saigo} [``Fractional integrals and derivatives of Mittag-Leffler type function'', Dokl. Akad. Nauk Belarusi 39, No. 4, 22--26 (1995)], and \textit{M. Sharma} and \textit{R. Jain} [Fract. Calc. Appl. Anal. 12, No. 4, 449--452 (2009; Zbl 1196.26013)] are special cases of the main results derived in this paper.