Multi-parametric mittag-leffler functions and their extension

By Anatoly A. Kilbas, A. Koroleva, Sergei Rogosin. 2013

70 citations recorded by the source corpus.

This paper surveys one of the last contributions by the late Professor Anatoly Kilbas (1948–2010) and research made under his advisorship. We briefly describe the historical development of the theory of the discussed multi-parametric Mittag-Leffler functions as a class of the Wright generalized hypergeometric functions. The method of the Mellin-Barnes integral representations allows us to extend the considered functions to the case of arbitrary values of parameters. Thus, the extended Mittag-Leffler-type functions appear. The properties of these special functions and their relations to the fractional calculus are considered. Our results are based mainly on the properties of the Fox H-functions, as one of the widest class of special functions.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/12ccbf6cab6213f8df159d1fe5e9e76c31fe24ca

Citations in the corpus

• A Note on Fractional Integral Operator Associated with Multiindex Mittag-Leffler Functions (2016, unknown): “[12–14, 16, 17] (see also [8] and [24]).”