Under the existence of model uncertainties and external disturbance, finite-time projective synchronization between two identical complex and two identical real fractional-order (FO) chaotic systems are achieved by employing FO sliding mode control approach. In this paper, to ensure the occurrence of synchronization and asymptotic stability of the proposed methods, a sliding surface is designed and the Lyapunov direct method is used. By using integer and FO derivatives of a Lyapunov function, three different FO real and complex control laws are derived. A hybrid controller based on a switching law is designed which has an efficient behavior than the each one of the designed controllers based on the minimization of an appropriate cost function. Numerical simulations are implemented for verifying the effectiveness of the methods.

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