A New Look at the Capacitor Theory

The mathematical description of the charging process of time-varying capacitors is reviewed and a new formulation is proposed. For it, suitable fractional derivatives are described. The case of fractional capacitors that follow the Curie-von Schweidler law is considered. Through suitable substitutions, a similar scheme for fractional inductors is obtained. Formulae for voltage/current input/output are presented. Backward coherence with classic results is established and generalised to the variable order case. The concept of a tempered fractor is introduced and related to the Davidson-Cole model.

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This article reviews the mathematical description of the charging process of time-varying capacitors and proposes a new formulation. Suitable fractional derivatives are described for it. The case of fractional capacitors that follow the Curie-von Schweidler law is considered. A similar scheme for fractional inductors is obtained through suitable substitutions. Formulae for voltage/current input/output are also presented. The backward coherence with classic results is established and generalized to the variable order case. The concept of a tempered fractor and its relation to the Davidson-Cole model are introduced.