Generalised fractional evolution equations of Caputo type

M.E. Hernández-Hernández, V.N. Kolokoltsov and L. Toniazzi

Chaos, Solitons & Fractals, 2017, vol. 102, issue C, 184-196

Abstract: This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations for the solutions. These results encompass known linear and non-linear equations from classical fractional partial differential equations such as the time-space-fractional diffusion equation, as well as their far reaching extensions.

Keywords: Fractional evolution equation; Generalised derivatives of Caputo type; Mittag–Leffler functions; Feller process; β-stable subordinator; Stopping time; Boundary point (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:102:y:2017:i:c:p:184-196

DOI: 10.1016/j.chaos.2017.05.005

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