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The inherent variability of renewable energy sources (RES) poses significant challenges for maintaining stable frequency and voltage in islanded hybrid microgrids (IHμGs). This variability increases system complexity and reduces overall inertia. This paper presents a control concept incorporating an improved fractional virtual inertia support scheme (FVIS) amid fractional tilt-derivative active disturbance rejection (TD-ADRC) controller for frequency and voltage containment. A comparative analysis is performed to evaluate system behavior with and without the conventional virtual inertia support (VIS). Moreover, Coot Optimization Technique (COT)-based TD-ADRC control framework is proposed for frequency and voltage adjustment. The suggested control approach is assessed under various practical conditions, including different uncertainties in load demand and the power output of RES. The effectiveness of the suggested control framework is evaluated in comparison with various established control methodologies presented in the literature. Finally, an eigenvalue trajectory-based stability assessment, including scenarios with communication latency, demonstrates the robustness of the proposed control configuration.