In this paper, we propose two novel cooperative-non-orthogonal-multiple-access (C-NOMA) and cooperative-rate-splitting-multiple-access (C-RSMA) schemes for uplink user cooperation. At the first mini-slot of these schemes, each user transmits its signal and receives the transmitted signal of the other user in full-duplex mode, and at the second mini-slot, each user relays the other user’s message with amplify-and-forward (AF) protocol. At both schemes, to achieve better spectral efficiency, users transmit signals in the non-orthogonal mode in both mini-slots. In C-RSMA, we also apply the rate-splitting method in which the message of each user is divided into two streams. In the proposed detection schemes for C-NOMA and C-RSMA, we apply a combination of maximum-ratio-combining (MRC) and successive-interference-cancellation (SIC). Then, we derive the achievable rates for C-NOMA and C-RSMA, and formulate two optimization problems to maximize the minimum rate of two users by considering the proportional fairness coefficient. We propose two power allocation algorithms based on successive-convex-approximation (SCA) and geometric-programming (GP) to solve these non-convex problems. Next, we derive the asymptotic outage probability of the proposed C-NOMA and C-RSMA schemes, and prove that they achieve diversity order of two. Finally, the above-mentioned performance is confirmed by simulations.