Some Alternative Solutions to Fractional Models for Modelling Power Law Type Long Memory Behaviours

Jocelyn Sabatier, Christophe Farges and Vincent Tartaglione
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Jocelyn Sabatier: IMS laboratory, Bordeaux University, UMR CNRS 5218, 351 Cours de la liberation, 33400 Talence, France
Christophe Farges: IMS laboratory, Bordeaux University, UMR CNRS 5218, 351 Cours de la liberation, 33400 Talence, France
Vincent Tartaglione: IMS laboratory, Bordeaux University, UMR CNRS 5218, 351 Cours de la liberation, 33400 Talence, France

Mathematics, 2020, vol. 8, issue 2, 1-16

Abstract: 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.

Keywords: fractional models; fractional differentiation; distributed time delay systems; Volterra equation; adsorption (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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