In dynamically changing environments, the spectrum-sharing method is a promising method to address the spectrum underutilization problem for cognitive radio (CR) systems. This paper investigates the capacity of cognitive radio multiple-access channel (CR-MAC) over a dynamic fading environment. Multiple secondary users (SUs) transmit to the secondary base station under the transmit power (TP) and interference temperature (IT) at the primary base station constraints. In order to perform a general analysis, a theoretical dynamic fading model termed hyper-fading model, which is suitable to the dynamic nature of cognitive radio channel, is considered. The optimal power allocation method is employed to maximize the capacity of CR-MAC for hyper-fading channel with TP and IT constraints and full channel side information. Through the numerical simulations, the capacity of the hyper-fading channels are compared with that of other channel fading models such as Rayleigh, Nakagami-2, and with an additive white Gaussian noise channel. Additionally, the impacts of the number of SUs on capacity is investigated.