This article studies congestion control of wireless access networks. In a wireless access network, it is necessary to design a robust active queue management (RAQM) technique to control congestion occurrence and to make the network robust simultaneously against some issues in the wireless link aspects, such as packet error rate (PER) and fading effects. On the other hand, a network is often described by a nonlinear model, in which the delayed packet drop probability is assumed as the input signal. So in this article, a RAQM technique is proposed based on an adaptive fractional order predictive sliding mode control (AFOPSMC) method, through which the following are achieved: (1) the stability of the nonlinear system with input delay is assured, (2) the congestion occurrence is prevented by controlling the queue measurement to the desired value, (3) the robustness against the external disturbances is achieved, and (4) the input signal obtained by the controller is limited between 0 and 1. In contrast to most recently published papers where input delay is ignored in the system description and input saturation is achieved through designing parameters, this article at first proposes a predictor to eliminate the input delay and then designs a compensated system to deal with the input signal constraint. Furthermore, the chattering phenomena, as a commonly caused issue in the sliding mode control, is eliminated based on the adaptive laws designed for the controller parameters. The theoretical results are validated and compared with some other related protocols through numerical simulations using Simulink and professional network simulator 2 (NS2).