Fractional control schemes are powerful tools for fulfilling robust tracking performance of different systems. This paper is the pioneering one in developing a fractional-order adaptive backstepping controller (FOABC) for a general class of integer-order and fractional-order (FO) systems. Model uncertainties and external disturbances can perturb system response and the controller is designed such that it can suppress the performance degradation caused by these factors. Moreover, rigorous mathematical analyses are carried out based on fractional Lyapunov theorems to ensure stability of the controlled systems. To justify the claims, worked-out examples including integer-order and FO systems are simulated. Good tracking performance of the proposed controller as well as robustness against uncertainties and insensitivity to external disturbances make it a good candidate for a broad range of systems. The results of implementing the proposed controller on different systems are compared with some newly proposed control approaches which highlight the outperformance of the FOABC.