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Atypical Case of the Dielectric Relaxation Responses and its Fractional Kinetic Equation

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Abstract

We present a probabilistic model of the microscopic scenario of dielectric relaxation relating to the atypical case of two-power-law responses.The surveyed approach extends the cluster model concept used for the description of the typical, Havriliak-Negami (HN) law. Within the proposed framework, all empirical two-power-law relaxation patterns may be derived. Their relaxation functions are expressed in terms of the three-parameter Mittag-Leffler function, and the kinetic equation takes the pseudodifferential form generalizing the Riemann-Louiville fractional calculus. This provides a clue to explain the universality observed in relaxation phenomena.

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Authors and Affiliations

  1. Institute of Radio Astronomy, National Academy of Sciences of Ukraine, 4 Chervonopraporna St., Kharkiv, 61002, Ukraine

    Aleksander Stanislavsky

  2. V.N. Karazin Kharkiv National University, Svobody Sq. 4, Kharkiv, 61022, Ukraine

    Aleksander Stanislavsky & Karina Weron

  3. Faculty of Fundamental Problems of Technology Wrocław, University of Technology Wybrzeże, Wyspiańskiego 27, Wrocław, 50-370, Poland

    Karina Weron

Authors
  1. Aleksander Stanislavsky
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  2. Karina Weron
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Correspondence to Aleksander Stanislavsky.

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Stanislavsky, A., Weron, K. Atypical Case of the Dielectric Relaxation Responses and its Fractional Kinetic Equation. FCAA 19, 212–228 (2016). https://doi.org/10.1515/fca-2016-0012

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  • DOI: https://doi.org/10.1515/fca-2016-0012

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