Probabilistic solutions to nonlinear fractional differential equations of generalized Caputo and Riemann–Liouville typeстатья
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Web of Science ,
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Дата последнего поиска статьи во внешних источниках: 27 октября 2021 г.
Авторы:
Hernández-Hernández M.E. ,
Kolokoltsov V.N.
Журнал:
Stochastics
Том:
90
Номер:
2
Год издания:
2018
Издательство:
Gordon and Breach Science Publishers
Местоположение издательства:
Switzerland
Первая страница:
224
Последняя страница:
255
DOI:
10.1080/17442508.2017.1334059
Аннотация:
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. © 2017 Informa UK Limited, trading as Taylor & Francis Group.
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Колокольцов Василий Никитич