Probabilistic solutions to nonlinear fractional differential equations of generalized Caputo and Riemann–Liouville type

M. E. Hernández-Hernández, V. N. Kolokoltsov

Research output

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)224-255
Number of pages32
JournalStochastics
Volume90
Issue number2
DOIs
Publication statusPublished - 17 Feb 2018

Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation

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