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
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Revised: 20 January 2020
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Accepted: 22 January 2020
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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.
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Keywords:
fractional models; fractional differentiation; distributed time delay systems; Volterra equation; adsorption
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MDPI and ACS Style
Sabatier, J.; Farges, C.; Tartaglione, V. Some Alternative Solutions to Fractional Models for Modelling Power Law Type Long Memory Behaviours. Mathematics 2020, 8, 196. https://doi.org/10.3390/math8020196
AMA Style
Sabatier J, Farges C, Tartaglione V. Some Alternative Solutions to Fractional Models for Modelling Power Law Type Long Memory Behaviours. Mathematics. 2020; 8(2):196. https://doi.org/10.3390/math8020196
Chicago/Turabian StyleSabatier, Jocelyn, Christophe Farges, and Vincent Tartaglione. 2020. "Some Alternative Solutions to Fractional Models for Modelling Power Law Type Long Memory Behaviours" Mathematics 8, no. 2: 196. https://doi.org/10.3390/math8020196
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