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The probabilistic point of view on the generalized fractional PDES
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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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Official URL: https://doi.org/10.1515/fca-2019-0033
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 | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science > Statistics | ||||||
| Library of Congress Subject Headings (LCSH): | Fractional calculus, Differential equations, Differential equations, Partial | ||||||
| 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: |
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| 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 | ||||||
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