Geodesic
Mixed Fractional Differential Equations and Generalized Operator-Valued Mittag-Leffler Functions
Matematičeskie zametki, Tome 106 (2019) no. 5, pp. 687-707

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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, Lévy subordinators.
Mots-clés : Dynkin's martingale 
@article{MZM_2019_106_5_a4,
     author = {V. N. Kolokoltsov},
     title = {Mixed {Fractional} {Differential} {Equations} and {Generalized} {Operator-Valued} {Mittag-Leffler} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {687--707},
     publisher = {mathdoc},
     volume = {106},
     number = {5},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_5_a4/}
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V. N. Kolokoltsov. Mixed Fractional Differential Equations and Generalized Operator-Valued Mittag-Leffler Functions. Matematičeskie zametki, Tome 106 (2019) no. 5, pp. 687-707. http://geodesic.mathdoc.fr/item/MZM_2019_106_5_a4/