Misyura A. Electromagnetic field in waveguides with fractal properties of sections

Purpose - development of mathematical model of the electromagnetic field in waveguides with fractal properties of sections. Object - the physical phenomena of propagation and interaction of electromagnetic waves with fractal boundaries of waveguides. Subject - amplitude, frequency and scaling dependences of the electromagnetic field characteristics. Methods - integro-differential fractional calculation and differintegral alpha-forms. Results - a new mathematical model of propagation process of electromagnetic waves in the guiding systems with fractal boundaries has been developed and applied. Novelty - the possibility of finding of eigenfunctions and eigennumbers of the boundary-value problems in rectangular waveguides with fractal boundaries has been proved; the interaction of electromagnetic waves with fractal impedance surfaces of the periodic systems has been appraised; the exact calculation of electrodynamics characteristics of the field in rectangular waveguides with fractal properties of sections has been first made; the thermodynamics paradoxes of energy dispersion, which arise up in artificial fractal mediums of the guiding systems, have been first considered. It is inculcated - educational process and research scientific work of the Zaporizhzhya national technical university. Sphere of the results use - Design office on development of the microwave frequency devices and antennas.