University of MaraghehSahand Communications in Mathematical Analysis2322-580703220160601On certain fractional calculus operators involving generalized Mittag-Leffler function334519751ENDinesh KumarDepartment of Mathematics \& Statistics, Jai Narain Vyas University, Jodhpur - 342005, India.0000-0001-5415-1777Journal Article20160104The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators are the generalization of the Saigo fractional calculus operators. The established results provide extensions of the results given by Gupta and Parihar [3], Saxena and Saigo [30], Samko et al. [26]. On account of the general nature of the generalized Mittag-Leffler function and generalized Wright function, a number of known results can be easily found as special cases of our main results.http://scma.maragheh.ac.ir/article_19751_f8cba31ae3575443d6bc568443f37036.pdf