Gabor transform of fractional kernels in radiation problems

Abstract

Exploring the application of fractional calculus in electromagnetic (EM) theory has been one of the subjects of our research interest. We have been utilizing some of the tools of fractional derivatives, fractional integrals, and in general fractionalization of some linear operators into electromagnetism and have been developing the area of fractional paradigm in EM theory. Among these problems, one was the possibility of the using fractionalization of certain operators in addressing some EM problems involving intermediate zones. In our previous study on this problem, our results described the mathematical techniques for fractionalizing the general kernels, which connect the near-zone fields to the far-zone fields for the planar, cylindrical, and spherical observation planes, and provided the physical roles of such fractional kernels in developing tools for analyzing the fields and potentials in intermediate zones. In the present study, we expand our investigation on these fractional kernels by studying the properties of their Gabor transformation in the two-dimensional (2D) radiation or scattering problems.