Based on the general theory of fractional order derivatives and integrals, application of the Caputo–Fabrizio operator is analyzed to improve a mathematical model of a two-mass system with a long shaft and concentrated parameters. Thus, the real transmission of complex electric drives, which consist of long shafts with a sufficient degree of adequacy, is presented as a two-mass system. Such a system is described by ordinary fractional order differential equations. In addition, it is well known that an elastic mechanical wave, propagating along a drive transmission with a long stiff shaft, creates a retardation effect on distribution of the time–space angular velocity, the rotation angle of the shaft, and its elastic moment. The approach proposed in the current work helps to take in account the moving elastic wave along the shaft of electric drive mechanism. On this basis, it is demonstrated that the use of the fractional order integrator in the model for the elastic moment enables it to reproduce real transient processes in the joint coordinates of the system. It also provides an accuracy equivalent to the model with distributed parameters. The distance between the traditional model and the model in which the fractional integral is used for the elastic moment modelling in a two-mass system, with a long shaft, is analyzed.

Within the scope of the presented work, a mathematical model of a prototype of a complex motion transmission on a ship was developed. The abovementioned motion transmission includes long elastic elements with distributed mechanical parameters. The system, containing the motion transmission under consideration, is driven by an engine via epicyclic gearing. The torque is transmitted via a long drive shaft to a propeller working with a variable blade geometry. The rotor of a synchronous generator is mounted on the ship’s long drive shaft. This shaft generator produces electricity that is fed to the ship’s electrical network. With the use of the developed mathematical model, electromechanical transients occurring during the transmission of mechanical power are analyzed. This paper analyzes the motion transmission with the use of computer simulation and presents the results of research.

The mathematical model of a fragment of a high-voltage electric network is developed in this paper. The network consists of a long power line with distributed parameters and an equivalent three-phase active-inductive load. Neumann and Robin—Poincare boundary conditions were used to identify the boundary conditions for the long line equation. The parameter output voltage (voltage at the end of the line) is introduced into the paper for further universal use of the developed line model. On the basis of the developed mathematical model, the program code is written in the algorithmic language Visual Fortran. By means of it, oscillograms of transient electromagnetic processes of voltages and currents in the form of spatial, temporal and temporal-spatial distributions during remote two-phase short circuits in the transmission line of high voltage are obtained. Two transient electromagnetic processes are analyzed in the present work. The first one was analyzed during the switching on of the line to the normal mode of operation with the subsequent transition to the emergency mode. The second one was analyzed during the switching on the line in the mode of a remote two-phase short circuit to the ground. The results of transient electromagnetic process simulation in the form of analyzed figures are shown. All the results presented in this paper were obtained exclusively using numerical methods.