SABATIER, Jocelyn

doi:10.3390/math10224184

Laboratoire de l'intégration, du matériau au système [IMS]

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Mathematics. 2022-11-09, vol. 10, n° 22, p. 4184

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This paper extends and illustrates a probabilistic interpretation of the fractional derivative operator proposed by Pr. José Tenreiro Machado. While his interpretation concerned the probability of finding samples of the derivate signal in the expression of the fractional derivative, the present paper proposes interpretations for other fractional models and more generally fractional behaviours (without using a model). It also proposes probabilistic interpretations in terms of time constants and time delay distributions. It shows that these probabilistic interpretations in terms of time delay distributions can be connected to the physical behaviour of real systems governed by adsorption or diffusion phenomena.< Leer menos

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Fractional behaviours

Probabilistic interpretations

Adsorption

Diffusion

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https://oskar-bordeaux.fr/handle/20.500.12278/172197

DOI

http://dx.doi.org/10.3390/math10224184

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IMS : Laboratoire de l'Intégration du Matériau au Système - UMR 5218

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Probabilistic Interpretations of Fractional Operators and Fractional Behaviours: Extensions, Applications and Tribute to Prof. José Tenreiro Machado’s Ideas

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