Adaptive Dual Synchronization of Fractional Order Chaotic Systems Under Caputo–Fabrizio Derivative with Multiple Disturbances and Unknown Parameters

This manuscript investigates the adaptive dual synchronization of fractional-order chaotic systems governed by the Caputo–Fabrizio operator, in the presence of multiple disturbances and indeterminate arguments. The systems under consideration are subject to various disturbances, including external perturbations and nonlinear uncertainties, whose upper bounds are unknown. First, a useful Caputo–Fabrizio fractional differential inequality is proposed, facilitating the efficient construction of an appropriate Lyapunov function. Furthermore, an effective sliding mode controller along with adaptive parameter laws is developed to regulate the fractional-order (hyper) chaotic systems. Finally, two numerical examples are presented to demonstrate the accuracy and effectiveness of the proposed method. These examples illustrate that the proposed control strategy is also applicable to both chaotic and hyperchaotic systems.