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Abstract-D B , DB and D B boundary conditions are used to investigate the resulting field patterns inside a parallel plate waveguide. The D B boundary conditions are accomodated by assigning the behavior of perfect magnetic conductor (PMC) for transverse electric mode (TE) and that of perfect electric conductor (PEC) for transverse magnetic (TM) mode, to the boundary, respectively. Likewise, DB boundary conditions are incorporated by assuming the behavior of boundary as PMC for both the TE mode and TM mode. Finally D B boundary conditions are realized by assigning PEC characteristic to the boundary for both TE and TM modes. A general wave propagating inside the parallel plate waveguide is assumed and decomposed into TE and TM modes for the purpose of analysis. Fractional curl operator has been used to study the fractional parallel plate D B , DB and D B waveguides for different values of fractional parameter α. Behavior of the field patterns in the waveguides are studied with respect to the fractional parameter α describing the order of the fractionalization.

Fractional dual solutions to the Maxwell equations for a dielectric slab placed in an unbounded dielectric magnetic medium are determined using the fractional curl operator. For extreme values of the intrinsic impedance of the host dielectric magnetic medium, the geometry becomes equivalent to that of a PEC or a PMC waveguide. In this way, the fractional dual fields for the PEC and PMC waveguide are also easily obtained.

In electromagnetics, a set of boundary conditions requiring vanishing of the normal components of the flux densities D and B (DB boundary) or their normal derivatives (D B boundary) have assumed great importance, recently. In the present study, we employ D B , DB and D B boundary conditions to investigate the fields in a three layered fractional dual planar waveguide. Middle layer of the waveguide is filled with air and other two layers are filled with chiral nihility metamaterial. Fractional dual solutions for the waveguide are obtained using a fractional curl operator with a parameter ' α ' defining the fractional order of the operator. For limiting values of the parameter, i.e., α = 0 and α = 1, the solutions to the Maxwell's equations correspond to the original and dual to the original solutions, respectively. Whereas, in general (0 < α < 1) , so called intermediate solutions are obtained. It has been noted that fields do exist in chiral nihility material backed by D B , DB or D B boundary, and a circular wave behaviour of the fields is observed in the core of the waveguide. In this sense DB , D B and D B chiral nihility waveguides behave identical to their DB counterpart.