This article investigates the mitigation of voltage-based power quality disturbances through dynamic voltage restorer (DVR). The proposed momentum adaption-based fractional least mean square (LMS) algorithm (ma-FLMS) with an additional feature of adaption term is implemented in updating the weight rule for estimating the reference load voltage in the control of DVR. The ma-FLMS has the property of updating the weight terms by employing the previously computed gradient in the current updated weight rule. This improves the accuracy of the estimated signal and convergence rate. The fractional-order proportional–integral–derivative (FOPID) is implemented to offer the more promising results for the generation of a reference control signal on the dc- and ac-link voltages. The meta-algorithm approach is employed to estimate the FOPID gains to reduce the computational effort. The autonomous group particle swarm optimizer (AGPSO) is used to demonstrate the results with high accuracy and convergence rate. Owing to the superior performance and flexibility in tuning, the proposed AGPSO-FOPID provides better settling time values, maximum overshoot, and undershoot of 0.14 s, 2.5%, and 5.6%. The proposed ma-FLSM with FOPID is tested under a variety of voltage disturbances and shows less steady-state error. The effectiveness is tested through simulation and experimental performance under different operating scenarios.