This article addresses the problem of designing an adaptive control for anesthesia. A simple fractional-order model is first proposed for anesthesia controller design. Parallel to this model, an identification algorithm is designed relying on Lyapunov stability theory to estimate the parameters in this model, and shown its ability to capture the behavior of the PK/PD model of the depth of anesthesia. Then an MRAC for anesthesia based on this simple model is designed, ensuring the stability and the convergence of the tracking error to zero. Fundamental to these designs is the Lyapunov Theory available in the literature and the extension of Barbalat Lemma for the integer-order systems to fractional-order systems proven in this paper. Simulations illustrate the effectiveness and robustness of the proposed control.