Some new Banach spaces are established. Based on those new Banach spaces and by using the coincidence degree theory, we present the existence results for a coupled system of nonlinear fractional differential equations with multipoint boundary value conditions at resonance case.

This paper investigates how opinion dynamics with memory effects and random communication uncertainties achieve consensus in an inhomogeneous Hegselmann–Krause (H-K) model. The Caputo fractional derivative is introduced to describe the influence of historical opinions, while multiplicative noise captures random disturbances in communication. We establish sufficient conditions under which all followers almost surely converge to the leader’s opinion. Moreover, we characterize the algebraic (power-law) convergence behavior determined by the fractional order. The analysis is based on fractional Lyapunov techniques and fractional Grönwall estimates, which enable the treatment of the nonlinear stochastic system with leadership. The results reveal how memory effects, leadership strength and stochastic perturbations jointly influence consensus formation. Numerical simulations are provided to verify the theoretical results and illustrate the effects of the model parameters on the convergence dynamics.

The pattern of single-mode and flat construction mode is very common to urban comprehensive transport center in China. In the course of planning and designing, it aims on convenient construction for various transport modes. There are not LOS evaluation system and comprehensive theory which prevent the high efficient from coming into being. LOS evaluation system and comprehensive theory would form based on the relation between passengers and transport mode joint or transfer facilities allocation, which aimed on passengers' need in UCPTH. LOS dynamics evaluation system of UCPTH would be used to evaluate, improve, re-assess and improve from construction stages to the operation stage.