In this paper, the design of the fractional-order predictive functional controller ((PFC)-P-alpha) for the linear fractional systems of arbitrary order has been presented. For this purpose, at first, the fractional order transfer function has been digitized via Grunwald-Letnikov definition to obtain the linear regression model of the system. Next, the non-minimal input-output fractional-order state space ((NMSS)-N-alpha) model of the system has been derived. The fractional-order predictive functional controller ((PFC)-P-alpha) has been then designed for the (NMSS)-N-alpha model structure via defining a fractional order cost function over the fractional-order non-minimal state vector. Finally, genetic algorithm (GA) has been employed to obtain the optimal (PFC)-P-alpha control coefficients. The fractional-order model of two rods thermal bench has been considered as the uncertain case study in this paper. Simulation results for temperature control of this fractional-order system are representative of better performance of the designed controller with respect to the NMSSPFC as well as the fractional GPC. (C) 2015 Elsevier Ltd. All rights reserved.