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On the probabilistic approach to the solution of generalized fractional differential equations of Caputo and Riemann-Liouville type
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Hernández-Hernández, Ma Elena and Kolokoltsov, V. N. (Vasiliĭ Nikitich) (2016) On the probabilistic approach to the solution of generalized fractional differential equations of Caputo and Riemann-Liouville type. Journal of Fractional Calculus and Applications, 7 (1). pp. 147-175. 14. ISSN 2090-584X.
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Official URL: http://fcag-egypt.com/Journals/JFCA/Vol7(1)_Papers...
Abstract
This paper provides a probabilistic approach to solve linear equa tions involving Caputo and Riemann-Liouville type derivatives. Using the probabilistic interpretation of these operators as the generators of interrupted Feller processes, we obtain well-posedness results and explicit solutions (in terms of the transition densities of the underlying stochastic processes). The problems studied here include fractional linear differential equations, well analyzed in the literature, as well as their far reaching extensions.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Journal of Fractional Calculus and Applications | ||||
Publisher: | Alexandria University * Faculty of Science | ||||
ISSN: | 2090-584X | ||||
Official Date: | 2016 | ||||
Dates: |
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Volume: | 7 | ||||
Number: | 1 | ||||
Page Range: | pp. 147-175 | ||||
Article Number: | 14 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) |
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