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.