Abstarct: Studying the complicated nonlinear behaviours such as chaos and its origins in dynamic systems like robot manipulators, leads to the expansion of our information towards increasing these systems efficiency and control. The objective of this thesis is to design a Fractional Dynamic Sliding Mode Controller (FDSMC) for chaotic two-lixnk Robot Manipulators. Due to its high precision and robustness against external disturbances and uncertainties, sliding mode control has attracted many research interests as an important and efficient strategy in nonlinear control. Dynamic sliding mode control is one of the generalized methods of sliding mode control and is baxsed on increasing the dynamics of the system. Because of using integrator in calculating the control signal, the chattering problem which is the most important problem in sliding mode controllers will be reduced significantly and it makes the control signal realizable for the robot. Nowadays, the special place of the fractional derivative as an appropriate tool in describing the systems better and also increasing the controllers’ capability is quite evident. Using such derivatives enables us to design a robust controller against uncertainties and disturbances, eliminate\ reduce the chattering problem along with maintaining and improving system desirable performance. Utilizing a fractional controller reduce chattering and increase the efficiency of the controller. The theoretical analysis and simulations have been carried out for chaotic robots under load and due to the time delay and in the presence of uncertainties and disturbances. Finally, the controller has been compared with three other types of controllers. Simulation results confirm the effectiveness of the proposed method.