In this paper, a novel controller designed for robust tracking control of a flexible-link manipulator operating in the presence of parameter uncertainties and external disturbances within the joint space is introduced. The proposed controller employs an adaptive sliding mode control approach, incorporating an improved barrier function, to ensure that trajectory errors remain within predefined performance bounds. This design enhances the tracking performance without overestimating control-switching gains. Additionally, a fixed-time adaptive sliding mode control, featuring a rapid nonsingular terminal sliding mode variable, is introduced to expedite the convergence rate of the system state during the initial stages. The efficacy of the proposed control scheme is established through the Lyapunov method, demonstrating finite-time convergence of the trajectory error to a specified neighborhood of zero. Experimental validation on a flexible-link system supports the effectiveness and advantages of the proposed control strategy, as evidenced via comparisons with two existing adaptive control schemes.