The theoretical derivation of optical time-domain fractional Fourier transformation is achieved and implemented. Based on the understanding of fractional Fourier transformation, we propose a new method for analyzing the influence of combined effects of dispersion and self-phase modulation on the propagation of optical pulses. And the simulation results show that when the dispersion is dominant in the transmission, a fractional Fourier transformation with a negative order number will help reduce the broadening of optical pulses induced by the dispersion. On the other hand, when the self-phase modulation is dominant, a positive order fractional Fourier transmission can help eliminate the pulse splitting effect.