2020/01/19 by Adrián Ricardo Gómez Plata, A. R. Gomez Plata, Plata, A. R. Gomez +7
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Applied mathematics #Cole–Cole equation #Debye–Hückel equation #Derivative (finance) #Dielectric #Differential equation #FOS: Physical sciences #Fractional Differential Equations Solutions #Fractional calculus #Function (biology) #Laplace transform #Material Dynamics and Properties #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Mittag-Leffler function #Monotone polygon #Physics #Quantum mechanics #Relaxation (psychology) #Statistical Mechanics (cond-mat.stat-mech) #Thermoelastic and Magnetoelastic Phenomena #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.2001.06856
published in arXiv (Cornell University) (Cornell University) · 20 pages
arxiv created 2020/01/19 · openalex publication_date 2020/01/19 · arxiv updated 2020/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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