The robotic manipulators are complex and coupled nonlinear systems. Therefore, the designing of an effective controller for these systems is quite complicated. The main hurdle in operating these systems is the inter-linkage between the links, and this can be removed by using any decoupling method. The decoupling between the links is not a good idea from the viewpoint of practical applications. In this paper, a fractional-order hybrid fuzzy logic controller (FOHFLC) scheme is developed for a two-degree-of-freedom rigid planar robotic manipulator with payload (2-DOF RPRMWP) plant for the trajectory tracking. The cuckoo search algorithm (CSA) is utilized for finding the optimal parameters of the proposed approach. For witnessing the effectiveness, the performance of proposed FOHFLC scheme is compared with integer-order hybrid FLC (IOHFLC) approach and conventional PID controller. The robustness testing is investigated for parameter variations and disturbance rejection for the proposed controller schemes.