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Fractal Fract
Volume 7
Issue 1
10.3390/fractalfract7010086
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Article

A New Look at the Capacitor Theory

by
Manuel Duarte Ortigueira
1,*,
Valeriy Martynyuk
2,
Volodymyr Kosenkov
2 and
Arnaldo Guimarães Batista
1
1
CTS-UNINOVA and DEE, NOVA School of Science and Technology of NOVA University of Lisbon, Quinta da Torre, 2829-516 Caparica, Portugal
2
Khmelnitsky National University, Instytutska, 11, 29016 Khmelnytskyi, Ukraine
*
Author to whom correspondence should be addressed.
Fractal Fract. 2023, 7(1), 86; https://doi.org/10.3390/fractalfract7010086
Submission received: 20 December 2022 / Revised: 8 January 2023 / Accepted: 10 January 2023 / Published: 12 January 2023
(This article belongs to the Special Issue Modern Mathematical Theories in Electromagnetism: Fractals, Wavelets and Fractional Operators)
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Abstract

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.
Keywords: fractional capacitor; fractional inductor; fractional derivative; fractor; Davidson–Cole model; tempered derivative fractional capacitor; fractional inductor; fractional derivative; fractor; Davidson–Cole model; tempered derivative

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MDPI and ACS Style

Ortigueira, M.D.; Martynyuk, V.; Kosenkov, V.; Batista, A.G. A New Look at the Capacitor Theory. Fractal Fract. 2023, 7, 86. https://doi.org/10.3390/fractalfract7010086

AMA Style

Ortigueira MD, Martynyuk V, Kosenkov V, Batista AG. A New Look at the Capacitor Theory. Fractal and Fractional. 2023; 7(1):86. https://doi.org/10.3390/fractalfract7010086

Chicago/Turabian Style

Ortigueira, Manuel Duarte, Valeriy Martynyuk, Volodymyr Kosenkov, and Arnaldo Guimarães Batista. 2023. "A New Look at the Capacitor Theory" Fractal and Fractional 7, no. 1: 86. https://doi.org/10.3390/fractalfract7010086

APA Style

Ortigueira, M. D., Martynyuk, V., Kosenkov, V., & Batista, A. G. (2023). A New Look at the Capacitor Theory. Fractal and Fractional, 7(1), 86. https://doi.org/10.3390/fractalfract7010086

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