The theory of fractal antennas requires a strict mathematical substantiation. With that end in view in the report are considered radiation of elemental fractal structured alpha-pole. Resonance properties of this radiator are immediate functions an alphapole moment of a current and fractal geometry. On the basis of introduced alphaforms various algorithms of a solution of a problem of the analysis and synthesis of geometry of a radiator with attraction of Hausdorff measure to which designing fractional integrals and derivatives are applied are stated.

The theoretical bases are developed for a method validation of electrodynamic similarity of fractally structured log-periodical alpha-pole antennas. The principle of similarity is formulated by language of the fractional order differential alpha-forms applied to the description of the artificial heterogeneous fractally structured medium.