A Fractional Model of Complex Permittivity of Conductor Media with Relaxation: Theory vs. Experiments

Abstract

Moving from the study of plasmonic materials with relaxation, in this work we propose a fractional Abraham–Lorentz-like model of the complex permittivity of conductor media. This model extends the Ciancio–Kluitenberg, based on the Mazur–de Groot non-equilibrium thermodynamics theory (NET). The approach based on NET allows us to link the phenomenological function of internal variables and electrodynamics variables for a large range of frequencies. This allows us to closer reproduce experimental data for some key metals, such as Cu, Au and Ag. Particularly, our fitting significantly improves those obtained by Rakic and coworkers and we were able to operate in a larger range of energy values. Moreover, in this work we also provide a definition of a substantial fractional derivative, and we extend the fractional model proposed by Flora et al.

Derivations of the stress-strain relations for viscoanelastic media and the heat equation in irreversible thermodynamic with internal variables

“…For this reason, in the following discussion, we will call these thermodynamical variables: dynamical variables since they have also been used, successfully, for the study of problems in dielectric and magnetic relaxation phenomena [19][20][21][22], diffusion and anelastic deformation [23][24][25][26][27][28][29][30][31][32]. It's important to note that the many theoretical results have been confirmed by the experimental data [33][34][35][36][37][38][39][40].…”

New Trends on the Mathematical Models and Solitons Arising in Real-World Problems

“…Mathematical models in science and technology have recently attracted an increased amount of research attention with the aim to understand, describe, and predict the future behaviors of natural phenomena. Recent studies on fractional calculus have been particularly popular among researchers due to their favorable properties when analyzing real-world models associated with properties such as anomalous diffusion, non-Markovian processes, random walk, long range, and, most importantly, heterogeneous behaviors [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. The concept of local differential operators along with power law settings and non-local differential operators were suggested in order to accurately replicate the above-cited natural processes.…”