Application of Fractional-Order Differential Operators for Enhanced Electromagnetic Field Modeling in Electrical Devices and Electromechanical Systems

Accurate mapping of electromagnetic field distributions is crucial in the analysis and design of electromechanical devices such as electric machines. Fractional calculus is a tool currently under development that allows classical models to be generalized by introducing fractional-order operators. This paper presents a theoretical framework for writing fractional-order differential operators in cylindrical and spherical coordinate systems by formulating fractional Lamé coefficients. The proposed approach allows for the consistent use of fractional derivatives in geometries commonly used in electromagnetic field modeling. Analytical examples illustrate the behavior of the derived operators and their consistency with the classical case for integer-order derivatives. The obtained results provide a theoretical basis for further research on field models using non-integer-order calculus and may in the future support the development of alternative methods for describing selected electromagnetic phenomena.