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Fractional Prabhakar Derivative and Applications in Anomalous Dielectrics: A Numerical Approach

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Theory and Applications of Non-integer Order Systems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 407))

Abstract

Fractional integrals and derivatives based on the Prabhakar function are useful to describe anomalous dielectric properties of materials whose behaviour obeys to the Havriliak–Negami model. In this work some formulas for defining these operators are described and investigated. A numerical method of product-integration type for solving differential equations with the Prabhakar derivative is derived and its convergence properties are studied. Some numerical experiments are presented to validate the theoretical results.

Work supported by the Cost Action CA15225.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Bari, Via E. Orabona 6, 70125, Bari, Italy

    Roberto Garrappa

  2. Dipartimento di Ingegneria Elettrica e dell’Informazione, Politecnico di Bari, Via E. Orabona 6, 70125, Bari, Italy

    Guido Maione

Authors
  1. Roberto Garrappa
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  2. Guido Maione
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Corresponding author

Correspondence to Roberto Garrappa .

Editor information

Editors and Affiliations

  1. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Artur Babiarz

  2. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Adam Czornik

  3. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Jerzy Klamka

  4. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Michał Niezabitowski

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Garrappa, R., Maione, G. (2017). Fractional Prabhakar Derivative and Applications in Anomalous Dielectrics: A Numerical Approach. In: Babiarz, A., Czornik, A., Klamka, J., Niezabitowski, M. (eds) Theory and Applications of Non-integer Order Systems. Lecture Notes in Electrical Engineering, vol 407. Springer, Cham. https://doi.org/10.1007/978-3-319-45474-0_38

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  • DOI: https://doi.org/10.1007/978-3-319-45474-0_38

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45473-3

  • Online ISBN: 978-3-319-45474-0

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