Abstract-New fractional boundary conditions (FBC) on plane boundaries are introduced. FBC act as intermediate case between perfect electric conductor and perfect magnetic conductor. In certain sense FBC are analogue of commonly used impedance boundary conditions with pure imaginary impedance. The relation between fractional order and impedance is shown. Plane wave diffraction problem by a strip described by FBC is formulated and solved using new method which extends known methods. Numerical results for physical characteristics are presented. Analyzing the scattering properties of the fractional strip new features are observed. FBC has one important special case where the fractional order equals to 1/2. For this special case the solution of diffraction problem can be found in analytical form for any value of wavenumber. Also for small values of wavenumber monostatic radar cross section has new specific resonances which are absent for other values of fractional order.

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