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The design of advanced robust control is crucial for serial robotic manipulators under various uncertainties and disturbances in case of the forceful performance needs of industrial robotic applications. Therefore, this work has proposed the design and implementation of a fractional order proportional tilt integral derivative (FOPTID) controller in joint space for a 3-DOF serial robotic manipulator. The proposed controller has been designed based on the fractional calculus concept to fulfill trajectory tracking with high accuracy and also reduce effects from disturbances and uncertainties. The parameters of the controller have been optimized with a GWO–PSO algorithm, which is a hybrid tuning method, by considering the time integral performance criterion. The superior and contribution of the GWO–PSO-based FOPTID controller has been demonstrated by comparing the results with those offered by PID, FOPID and PTID control strategies tuned by the GWO–PSO. The examination of the results showed that the proposed controller, which is based on the GWO–PSO algorithm, demonstrates better trajectory tracking performance and increased robustness against various trajectories, external disturbances, and joint frictions as compared to other controllers under the same operating conditions. In terms of the trajectory tracking performance for robustness, the superiority of the proposed controllers tuned by GWO–PSO has been confirmed by 20.2% to 44.5% reductions in the joint tracking errors. Moreover, for assessing the energy consumption of the tuned controllers, the total energy consumption of the proposed controller for all joints has been remarkably reduced by 2.45% as compared to others. Consequently, the results illustrated that the proposed controller is robust and stable and sustains against the continuous disturbance. Full article