## ON A FRACTIONAL INTEGRAL OPERATOR CONTAINING -GENERALIZED MITTAG LEFFLER FUNCTION IN ITS KERNEL AND PROPERTIES

## ON A FRACTIONAL INTEGRAL OPERATOR CONTAINING -GENERALIZED MITTAG LEFFLER FUNCTION IN ITS KERNEL AND PROPERTIES

*M. Singhal, E. Mittal*

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## 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.

## Keywords

-beta function, -hypergeometric function, -generalized Mittag-Leffler function, Mellin transform, generalized fractional integral operator.