On certain fractional calculus operators involving generalized MittagLeffler function
Article
English
OPEN
Dinesh Kumar
(2016)
 Publisher: University of Maragheh

Journal:
Sahand Communications in Mathematical Analysis
(issn: 23225807, eissn: 24233900)

Subject:
MarichevSaigoMaeda fractional calculus operators  Generalized MittagLeffler function  Generalized Wright hypergeometric function  Mathematics  QA1939
The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized MittagLeffler 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 MarichevSaigoMaeda 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 MittagLeffler function and generalized Wright function, a number of known results can be easily found as special cases of our main results.