A new class of fractional terminal sliding mode controller (FTSMC) is proposed for a class of nonlinear fractional order chaotic systems in this paper. The stability of the closed loop system is verified in the terms of the Lyapunov theorem. The proposed fractional controller design procedure leads to the convergence of the output tracking error toward the zero value in finite time, the robustness against external disturbance and uncertainty, and the reduction of chattering phenomenon. Two controller types of terminal sliding mode are introduced here comprising 1) a typical controller of terminal sliding mode and 2) a nonsingular controller of terminal sliding mode. Also, new theorems are provided here to facilitate designing procedure of robust controller. To assess the introduced approach, we applied the suggested controller to fractional Lorenz chaotic system. The simulation results, computed by MATLAB software, are able to explain the efficiency of the fractional terminal sliding mode controller Manuscript profile