I have not studied fractional Fourier Transforms but it looks like the concept may help other types of processing. It looks intriguing.
I found this file (fpft.m) at: http://www.mathworks.cn/matlabcentral/fileexchange/9200-partial-fast-fourier-transform?controller=file_infos&download=true
which also has a link to a descriptive .pdf file at: http://crd.lbl.gov/~dhbailey/dhbpapers/
(#16 and 17 or search "fractional fourier")
The paper explains the fractional FFT and applications. The matlab script uses it in a fast partial FFT algorithm. What is your application?