TY - JOUR ID - 19751 TI - On certain fractional calculus operators involving generalized Mittag-Leffler function JO - Sahand Communications in Mathematical Analysis JA - SCMA LA - en SN - 2322-5807 AU - Kumar, Dinesh AD - Department of Mathematics \& Statistics, Jai Narain Vyas University, Jodhpur - 342005, India. Y1 - 2016 PY - 2016 VL - 03 IS - 2 SP - 33 EP - 45 KW - Marichev-Saigo-Maeda fractional calculus operators KW - Generalized Mittag-Leffler function KW - Generalized Wright hypergeometric function DO - N2 - The 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. UR - https://scma.maragheh.ac.ir/article_19751.html L1 - https://scma.maragheh.ac.ir/article_19751_f8cba31ae3575443d6bc568443f37036.pdf ER -