MAAMRI, Nezha; TRIGEASSOU, Jean-Claude

doi:10.3390/fractalfract6100550

TRIGEASSOU, Jean-Claude
Laboratoire de l'intégration, du matériau au système [IMS]

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Fractal and Fractional. 2022-09-28, vol. 6, n° 10, p. 550

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The usual approach to the integration of fractional order initial value problems is based on the Caputo derivative, whose initial conditions are used to formulate the classical integral equation. Thanks to an elementary counter example, we demonstrate that this technique leads to wrong free-response transients. The solution of this fundamental problem is to use the frequency-distributed model of the fractional integrator and its distributed initial conditions. Using this model, we solve the previous counter example and propose a methodology which is the generalization of the integer order approach. Finally, this technique is applied to the modeling of Fractional Differential Systems (FDS) and the formulation of their transients in the linear case. Two expressions are derived, one using the Mittag–Leffler function and a new one based on the definition of a distributed exponential function.< Leer menos

Palabras clave

Initial value problem

Fractional differential systems

Fractional integral equation

Infinite state approach

Riemann–Liouville integral

Frequency distributed exponential function

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https://oskar-bordeaux.fr/handle/20.500.12278/172295

DOI

http://dx.doi.org/10.3390/fractalfract6100550

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

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A Plea for the Integration of Fractional Differential Systems: The Initial Value Problem

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Resumen en inglés

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URI

DOI

Centros de investigación