Hybrid implicit-explicit fractional transfer function simulation and system identification

Fractional order models are useful to model physical phenomena, such as batteries, fluid motion relaxation, heat transfers and even biomedical scenarios. Most of the proposed modelings are expressed in an explicit transfer function, meaning that the fractional differentiation is directly defined as an power of the Laplace variable. Early fractional order models such as the Cole-Cole model for dielectric relaxation belonged effectively to this type of models. However, there are also implicit transfer function models such as the Davidson-Cole ones, which prove to be useful and more accurate. One main drawback of implicit models is its difficulty related to time-domain simulation. The present study considers a hybrid transfer function model which includes both explicit and implicit terms. Frequency-domain analysis as well as time-domain simulation will be explored. Finally a practical aspect of system identification with a such explicit and implicit fractional model will be used by using time-domain data.