Fractional curl operator has been utilized to derive the fractional dual solutions for different planar boundaries. Perfect electric conductor (PEC), impedance, and perfect electromagnetic conductor (PEMC) planar boundaries have been investigated and the behavior of fractional dual solutions is studied with respect to the fractional parameter. The knowledge of fractional dual solutions has been extended by studying the fractional parallel plate waveguides, fractional transmission lines and the fractional rectangular waveguides. Fractional parallel plate waveguides with PEC, impedance, and PEMC walls as original problems have been studied for the field distribution inside the guide region and transverse impedance of the guide walls. The investigations have also been given for the fractional parallel plate chiro waveguides. Fractional transmission lines of symmetric and non-symmetric nature have been analyzed for their intermediate behavior and the impedance matching condition has been derived in terms of the fractional parameter. The fractional rectangular impedance waveguide has also been investigated. The fractional dual solutions and impedance have been compared with the reference results which have been found in good agreement for limiting values of the fractional parameter.