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.

当前的研究提出了一种新的分数阶三梯队供应链模型。证明了所提出模型的混沌行为，并在其同步后进行了研究。为此，为所提出的分数阶系统提供了一种新的控制技术。在控制器的设计中，假设模型的所有参数都是未知的。因此，所提出的滑模控制器配备了自适应机制，可以估计控制器的所有未知参数。基于Lyapunov稳定性定理和Barbalat引理，证明了系统的稳定性。为了提高所提出的控制器的性能并防止由于滑模控制器中的不连续函数而可能发生的颤振现象，模糊控制器与主控制器一起被提出。所提供的控制器不仅对不确定性具有鲁棒性，而且能够估计系统的参数并避免系统中的抖动。最后，通过数值结果证明了所提出的控制器在分数阶三梯队供应链系统同步方面的优异性能。