Abstract
The dynamic process represented by the fractional calculus is in nature dissipative, and the fractional constitutive equations have been successfully applied in describing the viscoelastic phenomena. In this paper, the fractional element for the dielectric relaxation, the cap-resistor, is introduced, and the basic fractional models of dielectric relaxation are constructed. The constitutive equations of the fractional models are derived, and their complex permittivities are presented. Analysis on the relaxation characteristics shows that these fractional models can offer relaxation processes with diverse frequency dependence, and some classical models such as Cole-Cole equation can be regarded as a special case of the fractional model. In addition, the fractional Poynting-Thomson model is used to simulate the dielectric relaxation behavior of glycerol, the fitting results show the model can delineate the dielectric constant and the dielectric loss very well.
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