Anomalous relaxation in dielectrics with Hilfer fractional derivative

2020/01/19 by Adrián Ricardo Gómez Plata, Ester C. A. F. Rosa, Plata, A. R. Gomez +5
Engineering · Materials Science · Mathematics · #FOS: Physical sciences #Fractional Differential Equations Solutions #Material Dynamics and Properties #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.2001.06856

openalex publication_date 2020/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new relaxation function depending on an arbitrary parameter as solution of a kinetic equation in the same way as the relaxation function introduced empirically by Debye, Cole-Cole, Davidson-Cole and Havriliak-Negami, anomalous relaxation in dielectrics, which are recovered as particular cases. We propose a differential equation introducing a fractional operator written in terms of the Hilfer fractional derivative of order ξ, with 0

Citations

• Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics
• A complex plane representation of dielectric and mechanical relaxation processes in some polymers

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