In this article, the position tracking control problem of a nonholonomic wheeled mobile robot with system uncertainties and external disruptions is examined. In the design control technique, a fractional-order sliding surface is presented for faster response of the dynamical system's states. Based on this sliding surface, a robust $H_{\mathrm{\infty }}$-based adaptive fractional-order sliding mode controller is developed to effectively handle the system's uncertainty and external disruptions. In the structure of the designed control scheme, the radial basis function neural network is utilized to reproduce the nonlinear function of the dynamical structure. The controller's $H_{\mathrm{\infty }}$ part compensates for the negative effects of the external disturbances and uncertainties robustly. The Lyapunov approach is used to determine the stability of the dynamical system. Furthermore, a numerical simulation analysis is carried out to show the effectiveness of the proposed control technique.