Fractional derivatives in electrical circuit theory – critical remarks

• Autorzy: Sikora R.

Identyfikatory

DOI

10.1515/aee-2017-0011

• Języki publikacji: EN

Abstrakty

EN

A number of critical remarks related to the application of fractional derivatives in electrical circuit theory have been presented in this paper. Few cases have been pointed out that refer to observed in selected publications violations of dimensional uniformity of physical equation rules as well as to a potential impact on the Maxwell equations.

Słowa kluczowe

EN

dimensional uniformity; physical equations; capacity; super capacitor

• Wydawca: Polish Academy of Sciences, Committee on Electrical Engineering
• Czasopismo: Archives of Electrical Engineering
• Rocznik: 2017
• Tom: Vol. 66, nr 1
• Strony: 155--163
• Opis fizyczny: Bibliogr. 17 poz., rys., wz.

Twórcy

autor

Sikora R.

• Department of Electrical Engineering West Pomeranian, University of Technology Sikorskiego 37, 70-313 Szczecin, Poland

Bibliografia

• [1] Sikora R., Fractional derivatives in electrical circuits theory – critical remarks, (in Polish), Electrical Review, no. 10, pp. 274-276 (2016).
• [2] Kaczorek T., Standard and Positive Electrical Circuits with Zero Transfer Matrices, Poznan University of Technology Academic Journals, no. 85 (2016).
• [3] Kaczorek T., Zeroing of state variables in fractional descriptor electrical circuits by state-feedbacks. Archives of Electrical Engineering, vol. 63(249), no. 3 (2014).
• [4] Kaczorek T., Positivity and Reachability of Fractional Electrical Circuits, Acta Mechanica et Automatica, vol. 5, no. 2 (2011).
• [5] Domek S., Application of fractional derivatives calculus in predictive control, (in Polish), West Pomeranian University of Technology Publishing, Szczecin (2013).
• [6] Domek S., Dworak P., Theoretical Developments and Application of Non-Integer Order Systems, Springer (2016).
• [7] Włodarczyk M., Zawadzki A., Positive order fractional derivatives in RLC circuits, (in Polish), Electrics, no. 1(217) (2011).
• [8] Zawadzki A., Włodarczyk M., Modelling of super capacitor’s charging and discharging processes, (in Polish), Measurements, Automatics, Control, vol. 56, no. 12, pp. 1413-1415 (2010).
• [9] Westerlund S., Ekstam L., Capacitor Theory, IEEE Transaction on Dielectric and Electrical Insulation, vol. 1, no. 5, pp. 826-839 (1994).
• [10] Morales M.A., Lainez R., Mathematical Modelling of Fractional Order Circuits, arXiv: 1602.03541v1 [physics. class-ph], vol. 21 (2016).
• [11] Povstenko Y., Solutions to time-fractional diffusion-wave equation in spherical coordinates, Acta Mechanica et Automatica, vol. 5, no. 2, pp. 108-111 (2011).
• [12] Gomez-Aguilar J.F., et al., Electrical circuits described by a fractional derivative with regular Kernel, Revista Mexicana de Fisica, vol. 62 (2016).
• [13] Sikora R., Chady T., Łopato P., Psuj G., Theoretical Electrical Engineering, (in Polish), West Pomeranian University of Technology Publishing, Szczecin (2016).
• [14] Sikora R., Electromagnetic field theory, (in Polish), WNT Warszawa (1997).
• [15] Gomez-Aguilar J.F., Behavior characteristics of a cap-resistor, memcapacitor, and a memristor from the response obtained of RC and RL electrical circuits described by fractional differential equations, Turkish Journal of Electrical Engineering & Computer Sciences, no. 24, pp. 1421-1433 (2016).
• [16] Erti H., Calik A.E., Sirin H., Sen M., Oder B., Investigation of electrical RC circuit within the framework of fractional calculus, Revista Mexicana de Fisica, vol. 61, pp. 58-63 (2015).
• [17] Kaku M., Einstein’s universe, (in Polish), Pruszynski & Co (2004).

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).