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Nowadays, the participation of renewable energy sources (RESs) and the integration of these sources with traditional power plants in microgrids (MGs) for providing demand-side power has rapidly grown. Although the presence of RESs in MGs reduces environmental problems, their high participation significantly affects the system's whole inertia and dynamic stability. This paper focuses on an islanded MG frequency regulation under the high participation of RESs. In this regard, a novel fractional order cascade controller (FOCC) is proposed as the secondary frequency controller. In the proposed FOCC controller structure, a fractional order proportional-integral controller is cascaded with a fractional order tilt-derivative controller. The proposed FOCC controller has a greater degree of freedom and adaptability than integer order controllers and improves the control system's efficiency. The adjustable coefficients of the proposed controller are tuned via the kidney-inspired algorithm. An energy storage system equipped with virtual inertia is also employed to improve the system inertia. The proposed FOCC controller efficiency is compared with proportional-integral-derivative (PID), tilt-integral-derivative (TID), and fractional order proportional-integral-derivative (FOPID) controllers under different disturbances and operating conditions. The results demonstrate that the presented controller provides better frequency responses compared to the other controllers. Moreover, the sensitivity analysis is performed to show the proposed controller robustness versus the parameters' changes in the system. [ABSTRACT FROM AUTHOR]