Fractional kernels and intermediate zones in electromagnetism: planar geometries

We have been interested in exploring the possibility of using fractional derivatives, fractional integrals, and/or generally some other fractionalized operators in treating certain problems in electromagnetics involving intermediate zones. For instance, it is well known that if we are given certain charge and/or current distributions in a finite-size volume (static or dynamic case), the electric potential and field quantities resulting from such a source can be expressed in terms of integrals involving the Green functions and the given source. We present the mathematical techniques for fractionalizing the general kernels for the planar geometries and discuss the physical significance of such fractional kernels in developing tools for analyzing the fields and potentials in intermediate zones.