Fractional Equations of Curie-von Schweidler and Gauss Laws

Abstract

The dielectric susceptibility of most materials follows a fractional power-law frequency dependence that is called the "universal" response. We prove that in the time domain this dependence gives differential equations with derivatives and integrals of noninteger order. We obtain equations that describe "universal" Curie-von Schweidler and Gauss laws for such dielectric materials. These laws are presented by fractional differential equations such that the electromagnetic fields in the materials demonstrate "universal" fractional damping. The suggested fractional equations are common (universal) to a wide class of materials, regardless of the type of physical structure, chemical composition or of the nature of the polarization.

11 pages, LaTeX

References in corpus (4)

• Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives
• Dynamics with Low-Level Fractionality
• Comparison of methods for estimating continuous distributions of relaxation times
• Signs of low frequency dispersions in disordered binary dielectric mixtures (50-50)

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• Fractional Dynamical Systems
• Origin of the Curie-von Schweidler law and the fractional capacitor from time-varying capacitance
• Fractional relaxation and wave equations for dielectrics characterized by the Havriliak-Negami response function
• Tempered relaxation with clustering patterns
• Evolution of Systems with Power-Law Memory: Do We Have to Die?