Abstarct: The adaptive fractional-order model reference control method baxsed on Lyapunov is recognized as an effective approach for controlling complex dynamic systems with uncertainty. By utilizing Lyapunov functions, this method guarantees the stability of the closed-loop system and adjusts the controller parameters online to bring the system output closer to the desired reference model output. This approach is particularly effective for fractional-order systems, which are commonly used to describe real-world phenomena. To enhance the performance of this method in the presence of significant uncertainty, a fractional-order dynamic component is added to the system. The new adaptive laws are derived using the Lyapunov method and Barbalat’s lemma, and a matrix inequality optimization problem is formulated to minimize the convergence error. Simulation results show that this method offers higher accuracy and performance compared to conventional approaches, while also reducing control effort.