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Mixed fractional differential equations and generalized operator-valued Mittag-Leffler functions. (English. Russian original) Zbl 1439.35538

Math. Notes 106, No. 5, 740-756 (2019); translation from Mat. Zametki 106, No. 5, 687-707 (2019).
Summary: 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.

MSC:

35R11 Fractional partial differential equations
33E12 Mittag-Leffler functions and generalizations
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