Extending our previous work for the planar case , in this Letter we present fractionalization of the kernels of integral transforms that link the field quantities over two coaxial cylindrical surfaces of observation for the two-dimensional (2-D) monochromatic wave propagation, and over two concentric spherical surfaces of observation for the 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. Like in the planar case , here the fractionalized kernels can supply another way of interpreting the fields in the intermediate zones.
Date of this Version
fractional kernels, fractional calculus, fractional paradigm, intermediate zone, electromagnetic waves
Date Posted: 25 July 2007
This document has been peer reviewed.