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An Application of Fractional Calculus to Dielectric Relaxation Processes

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Abstract

Recently fractional calculus has been successfully applied in the description of complex dynamics and proved to be a valuable tool for the solution of non-linear differential equations. In this study, an autocorrelation function obtained from the one-dimensional stochastic Ising model is assumed to be identical to the dipole correlation function of a molecular chain, and the fractional calculus method is applied to obtain a fractional diffusion equation derived from the stochastic Ising model applicable to the dielectric relaxation processes observed in polar materials. The equation is solved by using the Adomian decomposition method. At low temperatures, the solution of the equation is found to be compatible with the Cole–Cole and KWW (Kohlrausch–William–Watts) equations, and also with the algebraic decay relaxation function. Copyright © 2002 IFAC.

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Acknowledgements

We thank our friends Prof. Dr Kerim Kıymaç and Prof. Dr Metin Özdemir for their reading and correcting the article.

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Authors and Affiliations

  1. Department of Physics, Faculty of Arts and Sciences, Kastamonu University, Kastamonu, Turkey

    M. S. Çavuş

  2. Department of Physics, Faculty of Arts and Sciences, Çukurova University, Adana, Turkey

    S. Bozdemir

Authors
  1. M. S. Çavuş
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  2. S. Bozdemir
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Corresponding author

Correspondence to M. S. Çavuş .

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Editors and Affiliations

  1. Faculty of Art and Sciences, Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  2. Institute of Engineering, Department of Electrical Engineering, Polytechnic Institute of Porto, Rua Dr António Bernadino Almeida 431, Porto, 4200-072, Portugal

    José António Tenreiro Machado

  3. Edwardsville, School of Engineering, Southern Illinois University, Room: EB2064, Edwardsville, 62026-1805, USA

    Albert C. J. Luo

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Çavuş, M.S., Bozdemir, S. (2012). An Application of Fractional Calculus to Dielectric Relaxation Processes. In: Baleanu, D., Machado, J., Luo, A. (eds) Fractional Dynamics and Control. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0457-6_24

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  • DOI: https://doi.org/10.1007/978-1-4614-0457-6_24

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-0456-9

  • Online ISBN: 978-1-4614-0457-6

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