Analysis of fractional-order evolutionary behaviors between governments and logistics enterprises with interval parameters

Against the backdrop of global climate change and sustainable development, green logistics represents the core direction of logistics industry transformation. To handle the uncertainty of benefits and losses in the green transition, this paper introduces interval two-dimensional linear differential equations, and constructs integer-order (IO) and fractional-order (FO) evolutionary game models with interval parameters. It explores the government’s regulatory paths for the green transition of logistics enterprises under uncertain benefits and reward-punishment mechanisms. Based on stability theory, we analyze the government-enterprise evolutionary patterns and compare the two models under the static reward-penalty mechanism (SRPM). The results indicate that under SRPM, the two models exhibit consistent stability of boundary equilibrium points but differ in the stability of internal equilibrium points. For dynamic schemes, the interior equilibrium of the integer-order model is locally asymptotically stable (LAS) if subsidies are lower than fines. Under specific conditions, the upper and lower bounds of interval parameters affect the evolutionary stability of equilibrium points. This study provides theoretical support for the regulation of green transition in logistics.