Inner Electrodynamic Problem in Domains with Fractal Boundaries

In the present work, we apply the concept of fractional calculus to basic inner electromagnetics problem. The fractal approach it is applied to the analysis of surface impedance which arises on the surface of metamaterial plate in rectangular waveguide. The phenomenon testifies to possibility control of wave´s propagation in waveguides partly filled by artificial medium. The negative values of surface impedance correspond to negative values of inductivity and magnetic permeability that confirms our hypothesis about application of fractal mathematical model to description of metamaterial.