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A Fractional Complex Permittivity Model of Media with Dielectric Relaxation

1
Department of Biomedical and Dental Sciences and Morphofunctional Imaging, University of Messina, Via Consolare Valeria c/o A.O.U. Policlinico “G.Martino”, I, 98125 Messina, Italy
2
Engineering Office, Via Matteotti, 89044 Locri, Italy
*
Author to whom correspondence should be addressed.
Fractal Fract 2017, 1(1), 4; https://doi.org/10.3390/fractalfract1010004
Received: 11 August 2017 / Revised: 25 August 2017 / Accepted: 25 August 2017 / Published: 29 August 2017
(This article belongs to the Special Issue Fractional Dynamics)
In this work, we propose a fractional complex permittivity model of dielectric media with memory. Debye’s generalized equation, expressed in terms of the phenomenological coefficients, is replaced with the corresponding differential equation by applying Caputo’s fractional derivative. We observe how fractional order depends on the frequency band of excitation energy in accordance with the 2nd Principle of Thermodynamics. The model obtained is validated with respect to the measurements made on the biological tissues and in particular on the human aorta. View Full-Text
Keywords: fractional calculus; fractional ordinary differential equations; media with dielectric relaxation fractional calculus; fractional ordinary differential equations; media with dielectric relaxation
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Ciancio, A.; Flora, B.F.F. A Fractional Complex Permittivity Model of Media with Dielectric Relaxation. Fractal Fract 2017, 1, 4.

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