On certain fractional calculus operators involving generalized Mittag-Leffler function

Article English OPEN
Dinesh Kumar (2016)
  • Publisher: University of Maragheh
  • Journal: Sahand Communications in Mathematical Analysis (issn: 2322-5807, eissn: 2423-3900)
  • Subject: Marichev-Saigo-Maeda fractional calculus operators | Generalized Mittag-Leffler function | Generalized Wright hypergeometric function | Mathematics | QA1-939

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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