MULTIINDEX MITTAG-LEFFLER FUNCTIONS, RELATED GELFOND-LEONTIEV OPERATORS AND LAPLACE TYPE INTEGRAL TRANSFORMS ⁄

Recently, the interest in the Mittag-Le†er functions and their popularity have increased in view of their important role and applications in fractional calculus and related integral and difierential equations of fractional order. In this paper we introduce analogues of these functions, depending on two sets of multiple indices. We study their basic properties and relations with the operators of generalized fractional calculus. Corresponding generalized operators of integration and differention of the so-called Gelfond-Leontiev type, as well as Borel-Laplace type integral transforms, are also introduced and studied. This can be considered as a short survey exposition of results whose detailed proofs could be found in other author’s papers.