Abstract
The current study presents a new fractional-order three-echelon supply chain model. The chaotic behaviour of the proposed model is demonstrated, and after its synchronization is studied. To this end, a new control technique is offered for the proposed fractional-order system. In the design of the controller, it is assumed that all parameters of the model are unknown. Hence, the proposed sliding mode controller is equipped with an adaptive mechanism, which estimates all unknown parameters of the controller. On the basis of the Lyapunov stability theorem and Barbalat's lemma, the stability of the system is proven. In order to enhance the performance of the proposed controller and prevent the probable chattering phenomenon which could occur due to the discontinuous function in the sliding mode controller, a fuzzy controller is proposed along with the main controller. Not only is the offered controller robust against uncertainties, but also it is able to estimate parameters of the systems and avoids chattering in the system. Finally, the proposed controller's excellent performance for synchronization of the fractional-order three-echelon supply chain system is demonstrated through numerical results.