A Fractional Complex Permittivity Model of Media with Dielectric Relaxation

[摘要] In this work, we propose a fractional complex permittivity model of dielectric media with memory. Debye’s generalized equation, expressed in terms of the phenomenological coefficients, is replaced with the corresponding differential equation by applying Caputo’s fractional derivative. We observe how fractional order depends on the frequency band of excitation energy in accordance with the 2nd Principle of Thermodynamics. The model obtained is validated with respect to the measurements made on the biological tissues and in particular on the human aorta.

[学科分类] 数值分析

[关键词] fractional calculus;fractional ordinary differential equations;media with dielectric relaxation