On a fractional integral operator containing ?-generalized Mittag Leffler function in its kernel and properties

Abstract

This paper is devoted to the study of ?-generalized Mittag-Leffler function associated with ?-generalized beta function. We also obtain integral representations and other useful properties of it for example, Mellin transforms, recurrence relations etc. Further we develop derivative formulas and some fractional differ-integral properties for this ?-generalized Mittag-Leffler function. Other than this we also establish fractional integral operator containing ?-generalized Mittag-Leffler function as its kernel and obtain some associated properties.