This paper examines the nonholonomic mobile robot’s trajectory tracking control problem, considering external disturbances and the dynamical system’s uncertainties. The offered control technique presents a sliding surface of fractional-order to provide a quicker response from the controller. Utilizing the presenting sliding surface, a robust \(H_\infty \) -based fractional-order sliding mode controller is presented to efficiently handle these external influences to maintain the robust performance of the dynamical structure. The controller design employs a model-based control approach in conjunction with a \(H_\infty \) tracking control technique to reduce the negative effects of the uncertainties and external disturbances. Lyapunov’s stability criteria is used to demonstrate the stability of the dynamical system. Additionally, the numerical simulation results demonstrate the efficacy of the designed controller in a comparative manner.