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Mat. Zametki, 2019, Volume 106, Issue 5, Pages 687–707 (Mi mz12347)  

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

V. N. Kolokoltsov

University of Warwick

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.

Keywords: fractional derivative, operator-valued Mittag-Leffler function, potential operators, Dynkin's martingale, Lévy subordinators.

DOI: https://doi.org/10.4213/mzm12347

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English version:
Mathematical Notes, 2019, 106:5, 740–756

Bibliographic databases:

UDC: 517
Received: 07.02.2019

Citation: V. N. Kolokoltsov, “Mixed Fractional Differential Equations and Generalized Operator-Valued Mittag-Leffler Functions”, Mat. Zametki, 106:5 (2019), 687–707; Math. Notes, 106:5 (2019), 740–756

Citation in format AMSBIB
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\paper Mixed Fractional Differential Equations and Generalized Operator-Valued Mittag-Leffler Functions
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\vol 106
\issue 5
\pages 687--707
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\pages 740--756
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