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Mixed Fractional Differential Equations and Generalized Operator-Valued Mittag-Leffler Functions

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Abstract

We introduce the most general mixed fractional derivatives and integrals from three points of views: probability, the theory of operator semigroups, and the theory of generalized functions. The solutions to the resulting mixed fractional PDEs turned out to be representable in terms of of completely monotone functions in a certain class generalizing the usual Mittag-Leffler functions.

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Authors and Affiliations

  1. Department of Statistics, University of Warwick, Coventry, CV4 7AL, UK

    V. N. Kolokol’tsov

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  1. V. N. Kolokol’tsov
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Correspondence to V. N. Kolokol’tsov.

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Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 5, pp. 687-707.

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Kolokol’tsov, V.N. Mixed Fractional Differential Equations and Generalized Operator-Valued Mittag-Leffler Functions. Math Notes 106, 740–756 (2019). https://doi.org/10.1134/S0001434619110087

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  • DOI: https://doi.org/10.1134/S0001434619110087

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