Adaptive impulsive synchronization of fractional order chaotic system with uncertain and unknown parameters

• Proposed a novel method to realize the adaptive impulsive synchronization.
• Discussed fractional order chaotic systems with parameters uncertain and unknown.
• Applied the properties of solution of fractional order differential equation.
• Applied the Mittag-Leffter function in the proof.

Impulsive synchronization for fractional order chaotic system is a difficult problem that is required to solve. In this paper, a new method to realize the adaptive impulsive synchronization of two general fractional order chaotic systems with uncertain and unknown parameters is investigated. A new function is to be applied to the stability theory of fractional order directly. Then the impulsive synchronization of two fractional order chaotic systems with unknown parameters is discussed. The criteria for synchronization of the systems are established. Finally, some numerical examples are delivered to illustrate the effectiveness of our results.