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Probabilistic representation for the solutions of generalized fractional equations and generalized operator-valued Mittag-Leffler functions

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FDE2 - Fractional differential equations

2) Vassili Kolokoltsov Title: Probabilistic representation for the solutions of generalized fractional equations and generalized operator-valued Mittag-Leffler functions Astract: We present a unifying approach to theanalysis of generalized fractional Partial DifferentialEquations of Caputo-Djerbashian and Riemann-Liouville type. This point of view leads to the path integral representation for the solutions of these equations, which is seen to bestable with respect to the initial data and key parameters and is directly amenable to numeric calculations (Monte-Carlo simulation). In many casesthese solutions can be compactly presented via the wide class of operator-valuedanalytic functions of the Mittag-Leffler type, which are proved to beexpressed as the Laplace transforms of the exit times of monotone Markov processes.      

This talk is part of the Isaac Newton Institute Seminar Series series.

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