Based on the relation between the ambiguity function represented in a quasi-polar coordinate system and the fractional power spectra, the fractional Fourier transform moments are introduced. Important equalities for the global second-order fractional Fourier transform moments are derived and their applications for signal analysis are discussed. The connection between the local moments and the angle derivative of the fractional power spectra is established; this permits to solve the phase retrieval problem if only two close fractional power spectra are known.