This paper focuses on the adaptive trajectory tracking problem of near-space vehicles under dynamic coupling, parametric uncertainties, and input delays, which significantly degrade maneuverability and tracking precision. An intelligent adaptive control framework integrating backstepping techniques, neural network (NN) approximation, and a novel ordinary differential equation and partial differential equation (ODE-PDE) hybrid controller is proposed to address the problems. A backstepping procedure is systematically employed to stabilize the cascaded dynamics. Adaptive NNs with online learning are employed to counteract model uncertainties and coupled interactions. Additionally, a PDE-based predictor is introduced to reformulate delayed inputs, effectively mitigating the destabilizing effects of input delays. In the simulations, the proposed controller is compared with existing methods, demonstrating superior attitude tracking accuracy and enhanced system performance under input delays. The results confirm that the unified framework enhances adaptability to dynamic coupling and uncertainties, underscoring its potential for next-generation near-space flight systems, where resilience to complex aerodynamic interactions and hardware-induced latency is critical.