In this article, the plane wave diffraction by two strips is studied. Fractional boundary condition is required on strips when the fractional order for each strip is different. The goal of the paper is to investigate the resonant properties of such structures. The mathematical apparatus for the solution of the problem is given. The frequency dependency on the total radar cross-section is constructed for the different combinations of the fractional order. At the resonant frequencies, the near and the far-field distributions are presented.