Microgrids having renewable energies like wind and solar necessitate competent control and optimization to ensure system frequency stability. The intermittent behavior of the wind and solar influences the system frequency badly. This issue is appearing prominent in case of multi-interconnected microgrids. Hence, in this study, a fractional calculus-based integral tilt derivative with filter (ITDF)-based frequency regulation control strategy is utilized in a multi-microgrid. Here, the two unequal control zones with renewable energy and thermal generating power sources are connected through AC/DC parallel interfaces. A recent Jaya optimization method is exploited to tune the design variables of the controller. The comparative analyses of the dynamic response of the suggested control strategy with some existing control strategies like proportional integral derivative with filter (PIDF)/tilt integral derivative with filter (TIDF)/integral proportional derivative with filter (IPDF) exhibit the effectiveness of the suggested control strategy to suppress the frequency fluctuations. This paper also implements an accurate high-voltage direct current (AHVDC) line model and evaluates the results of the system by replacing conventional HVDC with AHVDC tie-line. Further, to enhance the frequency regulation, the inertia emulation controlling technique is executed which permits the exploitation of the accumulated energy in capacitors of HVDC interface for load frequency control. A comparative analysis shows the better dynamic response with AHVDC link with inertia emulation control strategy in parallel with AC link in comparison to conventional HVDC. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.