Journal
ENERGIES
Volume 13, Issue 21, Pages -Publisher
MDPI
DOI: 10.3390/en13215768
Keywords
circuit theory; circuit simulation; transmission lines; fractional calculus
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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 Grunwald-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.
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