Fractional derivative operators for modeling the dynamic polarization behavior as a function of frequency and electric field amplitude.

Polarization phenomena in ferroelectric materials are frequency-dependent, and the present article describes the use of a fractional derivative for the understanding of these phenomena as well as modeling them as functions of frequency and electric field amplitude. The focus was first directed toward the definition and validation of the proposed model through comparisons between simulations and measurements for high electrical field excitation amplitudes on a large frequency bandwidth (major hysteresis loops, measured over 4 decades). Subsequently, the same comparisons were made under ultra-weak as well as weak electric fields.