说明：  The generalized continuous wavelet transform associated with the fractional Fourier transform
(The main objective of this paper is to study the fractional Fourier transform (FrFT ) and the generalized continuous wavelet transform and some of their basic properties. Applications of the FrFT in solving generalized nth-order linear nonhomogeneous ordinary differential equations and a generalized wave equation are given. The generalized continuous wavelet transform, and its inversion formula, and the Parseval relation are also studied using the fractional Fourier transform.)