On fractional paradigm and intermediate zones in electromagnetism: II. Cylindrical and spherical observations

Extending our previous work for the planar case, in this letter, we present a fractionalization of the kernels of integral transforms that link the field quantities over two coaxial cylindrical surfaces of observation for two-dimensional (2-D) monochromatic wave propagation, and over two concentric spherical surfaces of observation for three-dimensional (3-D) wave propagation. With the proper radial normalizations, we show that the fractionalized kernels, with fractionalization parameter ν that here could attain complex values between zero and unity, can effectively be regarded as the kernels of the integral transforms that provide the radially normalized field quantities over the coaxial cylindrical surfaces (for 2-D case) and over the concentric spherical surfaces (for 3-D case) between the two original surfaces. As in the planar case, here, the fractionalized kernels can supply another way of interpreting the fields in the intermediate zones.