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Fractional Derivatives and Integrals: What Are They Needed For?
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Some Alternative Solutions to Fractional Models for Modelling Power Law Type Long Memory Behaviours

IMS laboratory, Bordeaux University, UMR CNRS 5218, 351 Cours de la liberation, 33400 Talence, France
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Mathematics 2020, 8(2), 196; https://doi.org/10.3390/math8020196
Received: 27 December 2019 / Revised: 20 January 2020 / Accepted: 22 January 2020 / Published: 5 February 2020
(This article belongs to the Special Issue Fractional Integrals and Derivatives: “True” versus “False”)
The paper first describes a process that exhibits a power law-type long memory behaviour: the dynamical behaviour of the heap top of falling granular matter such as sand. Fractional modelling is proposed for this process, and some drawbacks and difficulties associated to fractional models are reviewed and illustrated with the sand pile process. Alternative models that solve the drawbacks and difficulties mentioned while producing power law-type long memory behaviours are presented. View Full-Text
Keywords: fractional models; fractional differentiation; distributed time delay systems; Volterra equation; adsorption fractional models; fractional differentiation; distributed time delay systems; Volterra equation; adsorption
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Sabatier, J.; Farges, C.; Tartaglione, V. Some Alternative Solutions to Fractional Models for Modelling Power Law Type Long Memory Behaviours. Mathematics 2020, 8, 196.

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