Abstract: The nuclear reactor power control system is mainly used to control the start-stop of the reactor, power adjustment, and safe operation under accident conditions, and is one of the key systems for the safe operation of nuclear power plants. In most previous work, the classical neutron point kinetics model is adopted in the nuclear power control work. There also has been some researches based on the time-space fractional neutron point kinetics model since it was proposed in 2020. However, based on our current research, it did not attract widespread attention in the field of reactor power control. In this study, a nonlinear core model was established based on the fractional point reactor model and the thermo-hydraulic effect. The verification results of core dynamics show that the dynamic tunable characteristics make the model have a broad application prospect in the field of reactor engineering. Fuzzy control is one of the commonly used intelligent control methods. In the past, most of the research on the design of fuzzy controllers adopted a fixed universe, which made the controller less predictive of the system behavior, and the variable universe adaptive fuzzy FOPID controller could adjust the fuzzy universe range online according to the internal state of the system, and obtained better performance than the traditional FOPID controller. In this paper, a variable universe adaptive fuzzy FOPID controller was applied for the power control of a nuclear reactor based on the time-space fractional neutron point kinetics model, and the simulation under multi-transient conditions was carried out. The simulated working conditions include a power step change, where the reactor power increases from 100%FP to 110%FP and then decreases from 100%FP to 90%FP. Additionally, an external reactive perturbation test is conducted by introducing an external reactive perturbation of +50 pcm while operating at full power. There is also an internal parameter perturbation test, during which the internal parameters α_f, α_c, and β are varied by 10%, 20%, and 30%, respectively, at different time intervals under full power operation. Furthermore, the power is adjusted linearly, reduced from 100%FP to 25%FP and then increased back to 100%FP. The control rod speed limit for all the above working conditions is not more than 3 cm/s. The simulation results show that the proposed variable universe fuzzy fractional-order PID controller has no overshoot under all simulation conditions, has faster response time and control accuracy than the comparison controller, and has excellent anti-interference ability in the face of external reactive disturbances and changes in the internal parameters of the model.