Improved Order-Dependent Fixed-Time Stability of Fractional-Order Systems: Chaos Synchronization and Secure Image Encryption

This paper proposes a novel fixed-time synchronization criterion of Fractional-Order Chaotic Systems (FOCSs). First, for a class of Lyapunov functions whose derivatives are indefinite and coefficients are time-varying, two auxiliary functions are constructed. By combining the theory of fractional-order calculus, inequality techniques, and the method of contradiction, a fixed-time fractional-order stability theorem is derived. Second, the dependence of the settling-time on the order of the FOCSs is proved. Third, the synchronization control strategy with fractional-order term is designed to enhance the flexibility of the controller. Finally, the theoretical results are applied to Chua’s circuit and image encryption to illustrate the effectiveness of the proposed criterion.