A New Look at the Capacitor Theory

Manuel Duarte Ortigueira, Valeriy Martynyuk, Volodymyr Kosenkov, Arnaldo Guimarães Batista

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
37 Downloads (Pure)


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.

Original languageEnglish
Article number86
Number of pages18
JournalFractal and Fractional
Issue number1
Publication statusPublished - 12 Jan 2023


  • Davidson–Cole model
  • fractional capacitor
  • fractional derivative
  • fractional inductor
  • fractor
  • tempered derivative


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