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This study investigates the leader-following consensus problem in fractional-order multi-agent systems (MAS). First, a distributed observer is presented to estimate the state variables by using only the output information of MAS. Second, to overcome the difficulty of selecting an appropriate Lyapunov function for fractional order MAS, we propose a new state transformation technique to reconstruct the observer dynamic model. Then a new distributed frequency-dependent Lyapunov function is introduced in accordance with this model. Based on this new Lyapunov function, an adaptive vector backstepping controller design procedure is presented. Lastly, a series of virtual signals is generated to compensate for input nonlinearities including dead zones, quantization, and saturation by the fractional order auxiliary systems. Simulation results confirm the validity of the theoretical analysis.