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Chapitre D'ouvrage Année : 2022

Initial Value Problem Should Not Be Associated to a Fractional Model Description Whatever the Derivative Definition Used

Résumé

The paper shows that the Caputo definition of fractional differentiation is problematic if it is used in the definition of a fractional model and if initial conditions are taken into account. The demonstration is done using simple examples (or counterexamples). The analysis is extended to the Riemann-Liouville and Grünwald-Letnikov definitions. These results thus question the validity of results produced in the field of fractional model analysis in which initial conditions are involved.
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Dates et versions

hal-03717234 , version 1 (08-07-2022)

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Citer

Jocelyn Sabatier, Christophe Farges. Initial Value Problem Should Not Be Associated to a Fractional Model Description Whatever the Derivative Definition Used. Proceedings of the International Conference on Fractional Differentiation and its Applications (ICFDA’21), Springer International Publishing, pp.26-37, 2022, 978-3-031-04383-3. ⟨10.1007/978-3-031-04383-3_2⟩. ⟨hal-03717234⟩
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