What is the best argument of fractional Fourier transform over multiscale wavelet in data analysis purpose.

Optimization of the good time-frequency domain parameter ? "Good" will be, find the %time-%fq domain that minimize spectral entropy of the data.

Real physic world behavior, since particle-path is locally describe by fractional Fourier in N-slit problem context ?

Wavelet is just a fast log2 implementation of fractFt ?

Continuous transformation from time to frequency... But for what purpose ?

I take any strong argument of fracFt over wavelet