© 2020 Applied Computational Electromagnetics Society (ACES).In this article, there is considered the electromagnetic plane wave diffraction by the half-plane with fractional boundary conditions. As a mathematical tool, the fractional calculus is used. The theoretical part is given based on which the near field, Poynting vector and energy density distribution are calculated. Interesting results are obtained for the fractional order between marginal values, which describes a new type of material with new properties. The results are analyzed.