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Matematicheskie Zametki, 2019, Volume 106, Issue 5, Pages 687–707
DOI: https://doi.org/10.4213/mzm12347 (Mi mzm12347) 		 
This article is cited in 6 scientific papers (total in 6 papers)

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

V. N. Kolokoltsov

University of Warwick
Full-text PDF (571 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm12347
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.
Received: 07.02.2019
English version:
Mathematical Notes, 2019, Volume 106, Issue 5, Pages 740–756
DOI: https://doi.org/10.1134/S0001434619110087
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
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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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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