Control For A Class Of Fractional-order Chaotic Systems With Fractional-order In The (0, 2) Interval

With the in-depth study of the fractional-order dynamic systems, in recent years, chaotic phenomena has been found in many fractional-order nonlinear systems. Due to its potential applications in the field of science and engineering, more and more attention has been focused on dynamic analysis, control and synchronization of chaotic systems. However many previous synchronization methods for fractional-order chaotic systems only focused on the fractional-order 0 ?q ?1, a few results on synchronization of fractional-order chaotic systems with fractional-order 1 ?q ?2 have been considered. Hence, how to control and synchronize fractional-order chaotic systems with fractional-order 1 ?q ?2, which can complete the study of fractional-order chaotic systems.Motivated by the above considerations, in this paper, according the real-word physical systems, we propose the corresponding chaotic system and introduce a BLDCM system with fractional-order. The maximum Lyapunov exponent and chaotic attractors are discussed. The stabilization of the fractional-order chaotic BLDCM are achieved via a single input. Using the Lyapunov direct method, a control scheme is proposed to stabilize the FO-BLDCM chaotic system in the sense of Lyapunov. Furthermore, for the fractional-order chaotic systems with fractional-order in the(1, 2) interval, based on the two-parameter function of Mittag-Leffler and the generalized Gronwall inequality, the adaptive synchronization with partially or fully unknown parameters and the projective synchronization are discussed, some control schemes are given. The numerical simulations are given to verify the effectiveness of the proposed scheme.