<p>Current researches on modeling supply chain systems commonly neglect the inherent memory effect and heterogeneity within the supply chain. To bridge this gap, this paper constructs a novel incommensurate fractional-order chaotic supply chain system (IFCSCS). The numerical solutions are obtained by using the Adomian decomposition method. The dynamical behaviors under variations of fractional orders and parameters are investigated through spectral entropy complexity, bifurcation diagrams, and Lyapunov exponents. The results demonstrate that the appropriate selection of orders and parameters effectively suppresses chaotic behavior. Furthermore, the coupling synchronization between two IFCSCSs is achieved, as verified by simulations. The application of coupling synchronization enables rapid elimination of initial discrepancies and facilitates dynamic consistency.</p>