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

  • Roberto GarrappaEmail author
  • Guido Maione
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 407)


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.


Havriliak–Negami model Fractional derivative Prabhakar function Numerical method Product integration 


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di BariBariItaly
  2. 2.Dipartimento di Ingegneria Elettrica e dell’InformazionePolitecnico di BariBariItaly

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