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.

Original languageEnglish
Pages (from-to)740-756
Number of pages17
JournalMathematical Notes
Volume106
Issue number5-6
DOIs
StatePublished - 1 Nov 2019

    Research areas

  • Dynkin’s martingale, fractional derivative, Levy subordinators, operator-valued Mittag-Leffler function, potential operators

    Scopus subject areas

  • Mathematics(all)

ID: 51530009