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Multi-parametric mittag-leffler functions and their extension

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Abstract

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.

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Authors and Affiliations

  1. Faculty of Economics, Belarusian State University, Nezavisimosti ave, 4, Minsk, 220030, Belarus

    Anatoly A. Kilbas, Anna A. Koroleva & Sergei V. Rogosin

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  1. Anatoly A. Kilbas
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  2. Anna A. Koroleva
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  3. Sergei V. Rogosin
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Correspondence to Sergei V. Rogosin.

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Dedicated to Professor Francesco Mainardi on the occasion of his 70th anniversary

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Kilbas, A.A., Koroleva, A.A. & Rogosin, S.V. Multi-parametric mittag-leffler functions and their extension. fcaa 16, 378–404 (2013). https://doi.org/10.2478/s13540-013-0024-9

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