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Probabilistic solutions to nonlinear fractional differential equations of generalized Caputo and Riemann–Liouville type
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Hernández-Hernández, Ma Elena and Kolokoltsov, V. N. (Vasiliĭ Nikitich) (2018) Probabilistic solutions to nonlinear fractional differential equations of generalized Caputo and Riemann–Liouville type. Stochastics An International Journal of Probability and Stochastic Processes, 90 (2). pp. 224-255. doi:10.1080/17442508.2017.1334059 ISSN 1744-2508.
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Official URL: http://doi.org/10.1080/17442508.2017.1334059
Abstract
This paper provides well-posedness and integral representations of the solutions to nonlinear equations involving generalized Caputo and Riemann–Liouville type fractional derivatives. As particular cases, we study the linear equation with non constant coefficients and the generalized composite fractional relaxation equation. Our approach relies on the probabilistic representation of the solution to the generalized linear problem recently obtained by the authors. These results encompass some known cases in the context of classical fractional derivatives, as well as their far reaching extensions including various mixed derivatives.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
| Library of Congress Subject Headings (LCSH): | Fractional differential equations | ||||||||
| Journal or Publication Title: | Stochastics An International Journal of Probability and Stochastic Processes | ||||||||
| Publisher: | Taylor & Francis Ltd. | ||||||||
| ISSN: | 1744-2508 | ||||||||
| Official Date: | 2018 | ||||||||
| Dates: |
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| Volume: | 90 | ||||||||
| Number: | 2 | ||||||||
| Number of Pages: | 32 | ||||||||
| Page Range: | pp. 224-255 | ||||||||
| DOI: | 10.1080/17442508.2017.1334059 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
| Date of first compliant deposit: | 7 June 2017 | ||||||||
| Date of first compliant Open Access: | 5 June 2018 | ||||||||
| Funder: | University of Warwick Chancellor’s Interational Scholarship |
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