A class of fractional integral transforms: a generalization of the fractional Fourier transform

The paper presents a systematic and unified approach to fractional integral transforms. We introduce a new class of fractional integral transforms that includes the fractional Fourier and Hankel transforms and the fractional integration and differentiation operators as special cases. These fractional transforms may also be viewed as angular transforms, indexed by an angular parameter α, since their kernels are obtained by taking the limits of analytic functions in the unit disc along a radius making an angle α with the x-axis