In this paper,a novel single carrier equalization approach in the fractional Fourier domain(FRFD) is proposed.It can remove all the inter-symbol interference(ISI) and avoid the considerable noise enhancement of the frequency domain-zero forcing(FD-ZF) equalizer.As the fractional Fourier transform makes a chirp spread,the impulse response of the deep fading channel may be flattened in some orders of the FRFD while it would be greatly attenuated in the FD.By searching for an optimal order under certain criterion,we take advantages of the ZF algorithm to mitigate the effects of the ISI completely.This approach can overcome the contradiction between the ISI mitigation and the noise enhancement of the FD-ZF equalizer.Theoretical analysis and simulation results show that the proposed FRFD-ZF equalizer can achieve a significant performance and have the same computation cost O(N log N) as the conventional FD linear equalizer,especially in the frequencyselective deep-fading channels. In this paper, a novel single carrier equalization approach in the fractional Fourier domain (FRFD) is proposed. It can remove all the inter-symbol interference (ISI) and avoid the considerable noise enhancement of the frequency domain-zero forcing (FD-ZF ) equalizer. As the fractional Fourier transform makes a chirp spread, the impulse response of the deep fading channel may be flattened in some orders of the FRFD while it would be greatly attenuated in the FD.By searching for an optimal order under certain criterion, we take advantages of the ZF algorithm to mitigate the effects of the ISI completely. This approach can overcome the contradiction between the ISI mitigation and the noise enhancement of the FD-ZF equalizer. Theoretical analysis and simulation results show that the proposed FRFD-ZF equalizer can achieve a significant performance and have the same computation cost O (N log N) as the conventional FD linear equalizer, especially in the frequency selective deep-fading channels.