Journal
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES
Volume 90, Issue 2, Pages 224-255Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/17442508.2017.1334059
Keywords
Fractional differential equation; composite fractional relaxation equation; generalized Caputo type derivative; generalized Riemann-Liouville type derivative; boundary point; stable subordinator; Feller process
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Funding
- Chancellor International Scholarship through University of Warwick, UK
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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.
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