Abstarct: In this research, one of the methods of higher-order sliding mode control, along with defining the sliding surface as a nonsingular terminal sliding mode has been used using fractional-order calculus. In sliding mode control baxsed on fractional calculations, in defining the sliding surface and switching functions and also in defining the control laws, fractional-order derivatives and integrals are used. For this purpose, in this research, the design of a higher-order sliding mode method baxsed on fractional calculations has been used to improve the performance of robotic systems. Utilizing a higher-order sliding mode controller using the super-twisting algorithm and the fractional-order non-single terminal sliding mode for the two-lixnk serial robot is the novelty of the presented research. The design of the suggested controller is such that it is independent of the robotic manipulators model and is baxsed on system errors. Also, the design of the first-order fractional sliding mode controller has been done in this research and its results have been stated. In order to investigate the behavior of the designed controllers, the results of the proposed controller are compared with the proportional-derivative controller as well as the proportional-derivative-integral controller. Stability analysis of the close-loop system has performed using Lyapunov's method. The purposed of this research is achive to high accuracy, fast convergence, and high robustness in the closed-loop system.