Robot manipulators are extensively used to perform ultimate tasks (surgical, installation, transportation system, etc.) in different fields such as engineering, medical devices, and industry. Since these areas require high sensibility, control of robot manipulators is significant. Sliding mode control (SMC) is a robust control method used in non-linear systems due to its ability to cope with outer factors and parameter uncertainties. With technological improvements, the use of fractional order calculus has been upswing in recent years. In this study, a fractional order sliding mode controller was used to control a two-degree-of-freedom (2-DOF) robot manipulator. As fractional order operators, Grunwald-Letnikov and Caputo fractional order operators were applied. In this research, the comparison of the classical sliding mode controller with the Grunwald-Letnikov fractional order sliding mode controller (GLFOSMC) and Caputo fractional order sliding mode controller (CFOSMC) is discussed. According to the results obtained, it can be seen that CFOSMC performs better compared to GLFOSMC in terms of oscillation, stability at high step sizes, and control specifications such as settling time, rise time, and overshoot. Besides, the results show that the CFOSMC has significantly less error value compared to classical SMC and GLFOSMC.