Fractional calculus containing certain bivariate Mittag-Leffler kernel with respect to function

Abstract

In the present study, we introduce a general integral operator containing bivariate Mittag-Leffler (M-L) kernel with respect to a function tau ( z ) \tau \left(z) . This general family includes the usual, Hadamard, Katugampola, Erd & eacute;lyi-Kober, and Tempered versions for specific choices of the function tau ( z ) \tau \left(z) . We investigate the main properties of the general family by using series representation and conjugation relation.