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Meccanica

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13-03-2017 | New Trends in Dynamic and Stability

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

Authors: Michele Caputo, Mauro Fabrizio

Published in: Meccanica | Issue 13/2017

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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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Title: On the notion of fractional derivative and applications to the hysteresis phenomena
Authors: Michele Caputo
Mauro Fabrizio
Publication date: 13-03-2017
Publisher: Springer Netherlands
Published in: Meccanica / Issue 13/2017
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI: https://doi.org/10.1007/s11012-017-0652-y

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