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Electromagnetic-based derivation of fractional-order circuit theory

Abstract

In this paper, foundations of the fractional-order circuit theory are revisited. Although many papers have been devoted to fractional-order modelling of electrical circuits, there are relatively few foundations for such an approach. Therefore, we derive fractional-order lumped-element equations for capacitors, inductors and resistors, as well as Kirchhoff’s voltage and current laws using quasi-static approximations of fractional-order Maxwell’s equations. The proposed approach is not limited by the geometry of the considered lumped elements and employs the concepts of voltage and current known from the circuit theory. Finally, the proposed theory of circuit elements is applied to interpretation of Poynting’s theorem in fractional-order electromagnetism.

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Details

Category:
Articles
Type:
artykuł w czasopiśmie wyróżnionym w JCR
Published in:
Communications in Nonlinear Science and Numerical Simulation no. 79, pages 1 - 13,
ISSN: 1007-5704
Language:
English
Publication year:
2019
Bibliographic description:
Stefański T., Gulgowski J.: Electromagnetic-based derivation of fractional-order circuit theory// Communications in Nonlinear Science and Numerical Simulation. -Vol. 79, (2019), s.1-13
DOI:
Digital Object Identifier (open in new tab) 10.1016/j.cnsns.2019.104897
Verified by:
Gdańsk University of Technology

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