With the rapid advancement of low-cost electronics and control technologies, unmanned aerial vehicles (UAVs) are now widely used in many practical applications. However, controlling UAVs remains challenging because of their highly nonlinear dynamics, as well as the presence of external disturbances and model uncertainties. To handle these difficulties, sliding mode control (SMC) has become a popular choice for quadrotor UAVs due to its strong robustness against uncertainties and disturbances. But, conventional SMC often suffers from chattering, which can degrade control smoothness and affect actuator performance. To address this limitation, this paper proposes a fuzzy-based sliding mode control (FSMC) scheme for robust quadrotor trajectory tracking under model uncertainties and time-varying disturbances. The controller employs linear sliding surfaces for position and attitude dynamics. A fuzzy inference mechanism adaptively adjusts switching gains based on sliding variables and their derivatives. This adaptive tuning reduces switching intensity near desired trajectories and increases control action when tracking errors grow, thereby mitigating chattering while preserving robustness. Membership functions and rule base are designed to balance tracking accuracy and control effort. Lyapunov stability analysis proves global convergence of sliding surfaces and tracking errors. Numerical simulations in a MATLAB/Simulink environment, including parameter variations and disturbance scenarios, validate controller effectiveness. Compared with conventional PID control and feedback linearization, the proposed scheme achieves smoother control inputs, improved tracking performance, and total error reduction of up to 60%. These results indicate that adaptive fuzzy tuning enhances sliding mode performance while maintaining robustness, making the proposed approach suitable for practical UAV applications that require reliable operation under uncertain and dynamic conditions.