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In this paper, we investigate fairness of an uplink rate splitting multiple access (RSMA) system with randomly deployed users, which are modeled as a homogeneous Poisson Point Process. Specifically, randomly deployed users are divided into the central and edge groups, respectively. Two RSMA schemes are considered, namely, the cognitive radio-inspired RSMA (CR-RSMA) and rate fairness-oriented RSMA (RF-RSMA). In the CR-RSMA scheme, the quality of service (QoS) requirement of the primary user (PU) is given a priority, while the secondary user (SU) is served without affecting the outage performance of the PU. In the RF-RSMA scheme, by flexibly adjusting the SU’s power allocation factor to improve the rates fairness of users. Taking into account the user's QoS requirements, we first derive the closed-form expression for the outage probability of a user with a fixed location, and then we utilize a modified Jain's index to measure user fairness. Considering that the distance between the user and the base station (BS) affects the channel fading, the relative position of the user also impacts the RSMA performance. To reveal the effect of user's location on the outage performance and user fairness, we propose the distance-based user pairing strategies and obtain closed-form expressions for outage probabilities, which by using stochastic geometry. Simulation results validate the accuracy of the analytical indicates that, in the medium and high signal-to-noise ratio regions, the proposed RSMA schemes achieve better user fairness than the benchmark schemes.