Generalised Fractional Evolution Equations of Caputo Type

L. Toniazzi; M. E. Hern\'andez-Hern\'andez; V. N. Kolokoltsov

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Generalised Fractional Evolution Equations of Caputo Type

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

Analysis of PDEs · Submitted 1 Jun 2017

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The authors' main claim Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations for the solutions.

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arXiv ID1706.00319 (version 1)

Pith IDLKEPLEVV, Pith's permanent record of this paper and its review

CitationL. Toniazzi, M. E. Hern\'andez-Hern\'andez, V. N. Kolokoltsov. "Generalised Fractional Evolution Equations of Caputo Type." arXiv:1706.00319 (2017). https://pith.science/paper/LKEPLEVV

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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.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives.	contribution 0.77	0.56	0.06	asserted 0.94
s1	Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations for the solutions.	contribution 0.51	0.95	0.43	asserted 1.00
s2	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.	result 0.41	0.60	0.26	asserted 1.00
s3	\\ Meaning is given to a probabilistic generalisation of Mittag-Leffler functions.	contribution 0.69	0.74	0.08	asserted 0.99

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Original 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.

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For instance, a very standard example of the equation ([ref]), first studied by Schneider and Wyss [ref] and Kochubei [ref] (see also [ref] , [ref] , [ref] and references therein), is given by the time-fractional diffusion equation, where $-A= - 1/2 Δ$, $Δ$ being the Laplace operator.

Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics · Introduction · 0.82

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