In this paper we introduce a family of 3 m -index generalizations of the classical Mittag-Leffler functions. We study some basic properties of these new special functions, and thus find their order and type as entire functions, an asymptotic estimate, formulas for fractional and integer order difflerentiation and integration. The place of the 3 m -parametric functions among the other special functions of fractional calculus is emphasized, especially as Wright's generalized hypergeometric functions and Fox's H -functions. Some important special cases of the new functions are illustrated.
Key words: 3 m -parametric multi-index Mittag-Leffler functions, order and type of entire function, asymptotic formula, Mellin-Barnes-type integral representation, Riemann-Liouville fractional integral and derivative
Topic: MATHEMATICS