Problematic Applications of Fractional Derivatives in Electrotechnics and Electrodynamics

Can science exist without free discussion?

“…replaced with the following dependence: which can be found in Sikora and Pawłowski (2018b). The derivative operator in equation (8) is considered here within the meaning defined with equation (9) (see Appendix in Sikora and Pawłowski, 2018b) at the base point a = 0. Quantity σ provides an additional parameter expressed in time units, so the dimensional uniformity holds.…”

“…Quantity σ provides an additional parameter expressed in time units, so the dimensional uniformity holds. It is suggested in the Sikora and Pawłowski (2018b) that the dependence [equation (11)] can provide a description of an electrical circuit element, which combines both resistor and capacitor properties, for example, lossy capacitor of non-linear properties. Such an interpretation is supported by the cases for α = 1 [equation (11)] where it is just a standard Ohm`s law [equation (10)] for an ideal resistor, whereas for α = 0, the voltage u is proportional to the charge q , as it is in the case of the ideal capacitor.…”

“…The AEE commissioned me to review the article (Piotrowska, 2018), knowing my critical opinion on the use of fractional electrical engineering (Sikora, 2017b). Later in work of Sikora and Pawłowski (2018b), we wrote: “Literature on the subject provides two manners for fractional derivatives to be applied to physical problems, namely as: mathematical tool that allows to specifically solve certain physical equations, without modifying the equations and their parameters concerned; and modification to known physical relations by replacing the integer-order derivatives that occur there with the fractional derivatives. …”

The 21st Century Systems: An Updated Vision of Continuous-Time Fractional Models

“…Remark II.2. The question of the unities in fractional elements like coils and capacitors is an open subject [72], [73].…”

Archives of Electrical Engineering

“…Time delays can create many kinds of practical problems including the ones in positive electrical circuit systems, so it is necessary to study the properties of positive linear systems with delays. In the last decade, theoretical and applied researches of fractional calculus have achieved considerable advancements [4,5], and the application of the fractional derivative in the circuit is evaluated [6][7][8][9][10], which makes the field of the fractional circuit better. What's more, many problems in large-scale systems with delays have been widely studied.…”