Kolokoltsov, V. N. (Vasiliĭ Nikitich) (2019) The probabilistic point of view on the generalized fractional PDES. Fractional Calculus and Applied Analysis, 22 (3). pp. 543-600. doi:10.1515/fca-2019-0033

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Abstract

This paper aims at unifying and clarifying the recent advances in the analysis of the fractional and generalized fractional Partial Differential Equations of Caputo and Riemann-Liouville type arising essentially from the probabilistic point of view. This point of view leads to the path integral representation for the solutions of these equations, which is seen to be stable with respect to the initial data and key parameters and is directly amenable to numeric calculations (Monte-Carlo simulation). In many cases these solutions can be compactly presented via the wide class of operator-valued analytic functions of the Mittag-Leffler type, which are proved to be expressed as the Laplace transforms of the exit times of monotone Markov processes.

Item Type:	Journal Article
Divisions:	Faculty of Science > Statistics
Journal or Publication Title:	Fractional Calculus and Applied Analysis
Publisher:	Bulgarian Academy of Sciences, Institute of Mathematics and Informatics
ISSN:	1311-0454
Official Date:	30 July 2019
Dates:	Date Event 30 July 2019 Published 29 May 2019 Accepted
Date of first compliant deposit:	17 July 2019
Volume:	22
Number:	3
Page Range:	pp. 543-600
DOI:	10.1515/fca-2019-0033
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Copyright Holders:	© 2019 Diogenes Co., Sofia
Related URLs:	Publisher

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