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Mixed Fractional Differential Equations and Generalized Operator-Valued Mittag-Leffler Functions. / Kolokol’tsov, V. N.

в: Mathematical Notes, Том 106, № 5-6, 01.11.2019, стр. 740-756.

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Harvard

Kolokol’tsov, VN 2019, 'Mixed Fractional Differential Equations and Generalized Operator-Valued Mittag-Leffler Functions', Mathematical Notes, Том. 106, № 5-6, стр. 740-756. https://doi.org/10.1134/S0001434619110087

APA

Kolokol’tsov, V. N. (2019). Mixed Fractional Differential Equations and Generalized Operator-Valued Mittag-Leffler Functions. Mathematical Notes, 106(5-6), 740-756. https://doi.org/10.1134/S0001434619110087

Vancouver

Kolokol’tsov VN. Mixed Fractional Differential Equations and Generalized Operator-Valued Mittag-Leffler Functions. Mathematical Notes. 2019 Нояб. 1;106(5-6):740-756. https://doi.org/10.1134/S0001434619110087

Author

Kolokol’tsov, V. N. / Mixed Fractional Differential Equations and Generalized Operator-Valued Mittag-Leffler Functions. в: Mathematical Notes. 2019 ; Том 106, № 5-6. стр. 740-756.

BibTeX

@article{8a289e0ebd94418fb39f3fbc7317f180,
title = "Mixed Fractional Differential Equations and Generalized Operator-Valued Mittag-Leffler Functions",
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 = "Dynkin{\textquoteright}s martingale, fractional derivative, Levy subordinators, operator-valued Mittag-Leffler function, potential operators",
author = "Kolokol{\textquoteright}tsov, {V. N.}",
year = "2019",
month = nov,
day = "1",
doi = "10.1134/S0001434619110087",
language = "English",
volume = "106",
pages = "740--756",
journal = "Mathematical Notes",
issn = "0001-4346",
publisher = "Pleiades Publishing",
number = "5-6",

}

RIS

TY - JOUR

T1 - Mixed Fractional Differential Equations and Generalized Operator-Valued Mittag-Leffler Functions

AU - Kolokol’tsov, V. N.

PY - 2019/11/1

Y1 - 2019/11/1

N2 - 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.

AB - 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.

KW - Dynkin’s martingale

KW - fractional derivative

KW - Levy subordinators

KW - operator-valued Mittag-Leffler function

KW - potential operators

UR - http://www.scopus.com/inward/record.url?scp=85077095182&partnerID=8YFLogxK

U2 - 10.1134/S0001434619110087

DO - 10.1134/S0001434619110087

M3 - Article

AN - SCOPUS:85077095182

VL - 106

SP - 740

EP - 756

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 5-6

ER -

ID: 51530009