In this paper, a fractional order synchronous frame controller and its equivalent model, stationary frame control named fractional order proportional resonant controller, have been introduced using fractional order theory. Compared conventional proportional resonant controller, the proposed controller troller not only ensures a zero steady-state error for AC control systems, but also provides more robustness against fluctuations of resonant (center) frequency. Having a wider bandwidth and higher gain in the neighborhood of resonant frequency enhance the capability of this controller to deal with resonant frequency variations and furthermore, improve the time domain transient performance of these systems. Analog and digital implementions of this novel controller have been discussed. In addition, stability of the proposed controller has been investigated. Finally, the proposed fractional order control strategy is successfullyapplied to a grid-connected system as current regulator.