The mathematical description of the charging process of time-varying capacitors is reviewed and a new formulation is proposed. For it, suitable fractional derivatives are described. The case of fractional capacitors that follow the Curie–von Schweidler law is considered. Through suitable substitutions, a similar scheme for fractional inductors is obtained. Formulae for voltage/current input/output are presented. Backward coherence with classic results is established and generalised to the variable order case. The concept of a tempered fractor is introduced and related to the Davidson–Cole model.

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Modern electric vehicles typically exploit synchronous motors with magnetoelectric excitation as traction engines. While possessing a series of undeniable advantages, the synchronous motor has one significant drawback ‒ the high cost predetermined by the high price of permanent magnets. In addition, the impossibility to disable a magnetic field in case of engine malfunction can lead to an emergency on the road. Given this, there is a need to design new structures of electrical machines with electromagnetic excitation. The structure of a DC traction motor with electromagnetic excitation involving the rotor or stator segmentation makes it possible to considerably weaken the field of the armature transverse reaction by decreasing magnetic conductivity of the magnetic circuit in the transverse direction. Therefore, such a structure lacks commutating poles and a compensation winding. There are no permanent magnets in the structure, all windings are stationary, an electronic switch is used instead of a collector, and a windingless low-inertia rotor does not require additional measures to remove heat. That all has made it possible to significantly reduce the cost of active materials for the traction engine and improve its reliability. To test the performance of the new design, a full-size model of the engine and a working experimental prototype were fabricated. Applying a synchronous jet engine with magnetization for the BMW i3 electric car as an analog, the engine calculations were performed and its simulation was carried out. The results of the analysis show that the mass of the new engine is 35 % greater than the mass of the analog but the cost of active materials is less than that of the analog by 63 %. The results testify to the possibility of implementing a given structure industrially