In this article, there is considered a solution of the plane wave diffraction problem by one strip. The fractional boundary conditions are required on the surface of the strip. The strip with the complex valued fractional order boundary condition is studied. New type of the resonance is observed. The real and the complex part of the strip's impedance and dielectric permittivity of the strip are associated with the chosen complex valued fractional order. Numerical results for the near field, total radar cross section, relation between the fractional order and the impedance, dielectric permittivity of the strip are obtained.