EXTENDED MITTAG-LEFFLER FUNCTIONS ASSOCIATEDWITH WEYL FRACTIONAL CALCULUS OPERATORS

Abstract

This article deals with the family of extended Mittag-Leffler function in short ML-function defined in terms of extended Beta function, which depends upon the bounded sequence {κn}. The focus of the article is to define integral and differential operators of Weyl-type fractional operators associated with the proposed function. A new fractional calculus integral operator involving extended ML-function is also defined and its composition with the fractional calculus operators and some basic properties studied as well.