Kumar, D. (2016). On certain fractional calculus operators involving generalized Mittag-Leffler function. Sahand Communications in Mathematical Analysis, 03(2), 33-45.

Dinesh Kumar. "On certain fractional calculus operators involving generalized Mittag-Leffler function". Sahand Communications in Mathematical Analysis, 03, 2, 2016, 33-45.

Kumar, D. (2016). 'On certain fractional calculus operators involving generalized Mittag-Leffler function', Sahand Communications in Mathematical Analysis, 03(2), pp. 33-45.

Kumar, D. On certain fractional calculus operators involving generalized Mittag-Leffler function. Sahand Communications in Mathematical Analysis, 2016; 03(2): 33-45.

On certain fractional calculus operators involving generalized Mittag-Leffler function

^{}Department of Mathematics & Statistics, Jai Narain Vyas University, Jodhpur - 342005, India.

Abstract

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.

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