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.
