<p>In this paper, a hyperbolic cosine function-based flexible fixed-time stability result is proposed, and a fixed-time sliding mode controller is designed based on the result. Specifically, a global fixed-time stability result is presented by combining the power function with the hyperbolic cosine function, and a class of systems satisfying this result is proposed. Unlike traditional approaches, the settling time and convergence speed of these systems depend on fewer parameters. Next, the settling time function of the systems is analyzed, leading to the determination of parameter setting specifications. By appropriately selecting parameters, the system can be configured to trade off between faster convergence speed (i.e., shorter convergence time), more accurate convergence time estimation, or smaller initial convergence speed. Numerical analysis demonstrates the advantages of the proposed systems, and additional suggestions for parameter tuning are provided. Finally, a sliding mode control strategy is developed for second-order uncertain systems based on the proposed stability result. Theoretical analysis proves the stability of the closed-loop systems. Numerical simulations are presented to demonstrate the effectiveness of the proposed approach.</p>