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On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory

1
The Faculty of Mathematics, Physics and Informatics, University of Gdansk, 80-308 Gdansk, Poland
2
The Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, 80-233 Gdansk, Poland
3
SpaceForest Ltd., 81-451 Gdynia, Poland
*
Author to whom correspondence should be addressed.
Energies 2020, 13(21), 5768; https://doi.org/10.3390/en13215768
Received: 17 September 2020 / Revised: 30 October 2020 / Accepted: 31 October 2020 / Published: 4 November 2020
In this paper, concepts of fractional-order (FO) derivatives are reviewed and discussed with regard to element models applied in the circuit theory. The properties of FO derivatives required for the circuit-level modeling are formulated. Potential problems related to the generalization of transmission-line equations with the use of FO derivatives are presented. It is demonstrated that some formulations of FO derivatives have limited applicability in the circuit theory. Out of the most popular approaches considered in this paper, only the Grünwald–Letnikov and Marchaud definitions (which are actually equivalent) satisfy the semigroup property and are naturally representable in the phasor domain. The generalization of this concept, i.e., the two-sided fractional Ortigueira–Machado derivative, satisfies the semigroup property, but its phasor representation is less natural. Other ideas (including the Riemann–Liouville and Caputo derivatives—with a finite or an infinite base point) seem to have limited applicability. View Full-Text
Keywords: circuit theory; circuit simulation; transmission lines; fractional calculus circuit theory; circuit simulation; transmission lines; fractional calculus
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MDPI and ACS Style

Gulgowski, J.; Stefański, T.P.; Trofimowicz, D. On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory. Energies 2020, 13, 5768. https://doi.org/10.3390/en13215768

AMA Style

Gulgowski J, Stefański TP, Trofimowicz D. On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory. Energies. 2020; 13(21):5768. https://doi.org/10.3390/en13215768

Chicago/Turabian Style

Gulgowski, Jacek, Tomasz P. Stefański, and Damian Trofimowicz. 2020. "On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory" Energies 13, no. 21: 5768. https://doi.org/10.3390/en13215768

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