ON CERTAIN FRACTIONAL CALCULUS OPERATORS INVOLVING GENERALIZED MITTAG-LEFFLER FUNCTION

The object of this paper is to establish certain general- ized fractional integration and di erentiation involving generalized Mittag-Le er function de ned by Salim and Faraj [25]. The consid-ered generalized fractional calculus operators contain the Appell's function F3 [2, p.224] as kernel and are introduced by Saigo andMaeda [23]. The Marichev-Saigo-Maeda fractional calculus opera- tors 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-Le er func- tion and generalized Wright function, a number of known resultscan be easily found as special cases of our main results.