Abstract
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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Sabatier, J., Farges, C. (2022). Initial Value Problem Should Not Be Associated to a Fractional Model Description Whatever the Derivative Definition Used. In: Dzielinski, A., Sierociuk, D., Ostalczyk, P. (eds) Proceedings of the International Conference on Fractional Differentiation and its Applications (ICFDA’21). ICFDA 2021. Lecture Notes in Networks and Systems, vol 452. Springer, Cham. https://doi.org/10.1007/978-3-031-04383-3_2
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DOI: https://doi.org/10.1007/978-3-031-04383-3_2
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