Triple-K And Penta-K Extended Forms Of Some Generalized Forms Of Mittag-Leffler Functions And Their Hadamard K-Fractional Integrals

Abstract

In this work, a extended form of a generalized form of the classical beta function is introduced. Moreover; a triple extended form and a penta  extended form, based on the extended beta function, of some generalized forms of the classical Mittag-Leffler function, are introduced. Furthermore, the Hadamard fractional integrals of some functions involving these extended Mittag-Lefflers functions are found.