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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jocelyn Sabatier & Christophe Farges & Vincent Tartaglione, 2020. "Some Alternative Solutions to Fractional Models for Modelling Power Law Type Long Memory Behaviours," Mathematics, MDPI, vol. 8(2), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:196-:d:316900
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    Citations

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    Cited by:

    1. Jocelyn Sabatier, 2022. "Probabilistic Interpretations of Fractional Operators and Fractional Behaviours: Extensions, Applications and Tribute to Prof. José Tenreiro Machado’s Ideas," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    2. Ishtiaq Ali & Sami Ullah Khan, 2023. "A Dynamic Competition Analysis of Stochastic Fractional Differential Equation Arising in Finance via Pseudospectral Method," Mathematics, MDPI, vol. 11(6), pages 1-16, March.

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