Based on the fractional calculus theory, in the absence of external driving force, the fractional transport model of asymmetric coupling particle chain in symmetric periodic potential is established. Using the method of fractional difference, the model is solved numerically and the influences of the various system parameters on directional transport velocity are discussed. Numerical results show that in the case without external force and noise-driven, the fractional asymmetric coupling system can still generate directional transport, and the transport velocity increases as fractional order increases. When the fractional order is fixed, the average velocity of the particle chain varies non-monotonically with coupling strength and barrier height. In the case with noise, the generalized stochastic resonance phenomenon occurs. Besides, we can make the noise not affect the system or even promote directional transport by adjusting other parameters.