Multi-Microgrids (MMGs) provide a highly promising approach for accommodating diverse distributed energy resources and improving the overall system performance. This enhanced performance encompasses aspects such as reliability, resilience, flexibility, and energy efficiency. As MMGs become more prevalent, the conventional centralized control approach struggles to adequately address the coordinated operation of system. Therefore, this article proposes a leader-follower-based distributed control strategy (DCS) for coordinated frequency control of numerous heterogeneous and geographically dispersed DERs in MMG network. The DCS employs a robust nonlinear fractional-order proportional integral derivative controller for frequency control of MMG. To optimize the parameters of the controller, an adaptive hybrid chaotic atom search-particle swarm optimization (ACAS-PSO)-based distributed intelligent technique is proposed. Initially, the proposed control strategy efficacy has been tested against various single/multidimensional benchmark functions. Then, it is applied to optimize the parameters of the controller for frequency regulation of MMG system by minimizing the integral absolute error (IAE). The findings obtained illustrate that the proposed ACAS-PSO control technique has an IAE improvement of 42.21 % to 65.3 % in MG 1, 55 % to 96 % in MG 2 and 42.2 % to 84.5 % in MG 3 compared to state-of-the-art. Moreover, the proposed method enhances the frequency response in terms of settling time by 23.4 % to 68.7 % in MG 1, 45.2 % to 68.3 % in MG 2 and 36.35 % to 48 % in MG 3, and the control effort is enhanced by 31.2 % to 87.6 % in MG 1, 31.3 % to 87.05 % in MG 2 and 31.25 % to 73.2 %, in MG 3 compared to other techniques presented. In addition, the robustness of the proposed DCS is validated against plug-and-play ability, communication failure, and delays. Further, the proffered controller is validated by implementing in real-time digital simulation using OPAL-RT.