In this paper, a fractional-order sliding mode control approach for position tracking control of robot manipulators is designed. By designing a fractional-order sliding manifold, a fractional-order sliding mode-based control approach is designed to handle system uncertainties and external disruptions robustly. The designed controller uses radial basis function neural network to reproduce the non-linearity of dynamic structure. The adaptive bound component of the controller handles reconstruction error and estimates the upper limits on external disturbances. The stability of the proposed control approach is analyzed through Lyapunov stability criteria and Barbalat’s lemma. As a result of the proposed controller, an asymptotic error convergence is achieved, and the efficiency of the controller is enhanced. Moreover, the validity of the presented control approach is shown by simulation studies.