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In today's sophisticated global marketplace, supply chains are complex nonlinear systems in the presence of different types of uncertainties, including supply-demand and delivery uncertainties. Though up to now, some features of these systems are studied, there are still many aspects of these systems which need more attention. This necessitates more research studies on these systems. Hence, in this study, we propose a variable-order fractional supply chain network. The dynamic of the system is investigated using the Lyapunov exponent and bifurcation diagram. It is demonstrated that a minor change in the system's fractional-derivative may dramatically affect its behavior. Then, distributed consensus tracking of the multi-agent network is studied. To this end, a control technique based on the sliding concept and Chebyshev neural network estimator is offered. The system's stability is demonstrated using the Lyapunov stability theorem and Barbalat's lemma. Finally, through numerical results, the proposed controller's excellent performance for distributed consensus tracking of multi-agent supply chain network is demonstrated. [ABSTRACT FROM AUTHOR]

This study is concerned with dynamical investigation, electrical circuit realization, and emulation of a fractional three-echelon supply chain system. In the financial realm, long-term memory effects play important roles. On the other hand, most financial systems are uncertain with unknown nonlinear dynamics. However, most studies on nonlinear supply chains neither consider the fractional calculus nor take advantage of state-of-the-art emulation methods. These issues motivated the current study. A fractional-order chaotic three-echelon supply chain system is studied. At first, the system's dynamic is studied through Lyapunov exponent and bifurcation diagrams. It is shown that a slight deferent in some parameters of the system can dramatically change the behavior of the system. Then, a real-time analog circuit is designed and implemented to investigate the system's chaotic behavior. This way, the system's chaotic attractors are empirically demonstrated. Finally, emulation and interpolation of the fractional-order chaotic system using the Gaussian process have been studied, and its luminous results have been presented. [ABSTRACT FROM AUTHOR]