  In this paper, synchronization of fractional order Coullet system with
precise and also unknown parameters are studied. The proposed method which is
based on the adaptive backstepping, has been developed to synchronize two
chaotic systems with the same or partially different attractor. Sufficient
conditions for the synchronization are analytically obtained. There after an
adaptive control law is derived to make the states of two slightly mismatched
chaotic Coullet systems synchronized. The stability analysis is then proved
using the Lyapunov stability theorem. It is the privilege of the approach that
only needs a single controller signal to realize the synchronization task. A
numerical simulation verifies the significance of the proposed controller
especially for the chaotic synchronization task.
