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On the notion of fractional derivative and applications to the hysteresis phenomena

  • New Trends in Dynamic and Stability
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Abstract

In the first part of the paper, we discuss on the general properties of a fractional derivative. In particular we found that the definition presented in Caputo and Fabrizio (Prog Fract Differ Appl 1(2):73–85, 2015) satisfies these general conditions, including the non-locality. So by means of numerical simulations we have shown different behaviors of this new operator with respect to Caputo’s derivative. In particular we have shown that the memory effects are less evident when we consider the new derivative. Finally, in the second part, a model for the study of the magnetic hysteresis phenomena is presented. The thermodynamic compatibility is proven, and a checking of the model is tested with some numerical simulations.

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Authors and Affiliations

  1. College of Geoscience, Texas A&M University, College Station, TX, USA

    Michele Caputo

  2. Dipartimento di Matematica, Università di Bologna, Piazza Porta S. Donato 5, 40126, Bologna, Italy

    Mauro Fabrizio

Authors
  1. Michele Caputo
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  2. Mauro Fabrizio
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Corresponding author

Correspondence to Mauro Fabrizio.

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Conflicts of interest

Author M. Fabrizio is a member of the Editorial Board of Meccanica. But this paper is presented for the Special Issue “New trends in Dynamic and Stability. So there is no conflict exists. In any case the authors declare that they have no conflict of interest.

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Caputo, M., Fabrizio, M. On the notion of fractional derivative and applications to the hysteresis phenomena. Meccanica 52, 3043–3052 (2017). https://doi.org/10.1007/s11012-017-0652-y

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  • DOI: https://doi.org/10.1007/s11012-017-0652-y

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