Generalised Fractional Evolution Equations of Caputo Type

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. \\ Meaning is given to a probabilistic generalisation of Mittag-Leffler functions.

arXiv commentTo be published in 'Chaos, Solitons & Fractals'

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• Fast exact simulation of the first passage of a tempered stable subordinator across a non-increasing function
• Censored Stable Subordinators and Fractional Derivatives
• Fast exact simulation of the first-passage event of a subordinator
• Self-similar Cauchy problems and generalized Mittag-Leffler functions
• Time Fractional Poisson Equations: Representations and Estimates
• Mixed linear fractional boundary value problems