The family of fractional Fourier transforms permits presentation of a temporal signal not only as a function of time or as a pure frequency function but also as a mixed time and frequency function with a continuous degree of emphasis on time or on frequency features. We show how it is possible to implement the fractional Fourier transform on time signals by using optoelectronic modulators and optical fibers with suitable dispersion. We also show how a fractional-Fourier-transform-based photonic signal-processing system could be composed.