Abstract
This research work aims at investigating the fractional-order genetic regulatory networks (FOGRNs) with feedback regulation delays. First, we have established the existence and uniqueness of considered systems based on the Banach fixed point theorem. Second, based on a Lyapunov method and fractional-order Razumikhin theorem, some novel sufficient criteria are obtained to ensure the global asymptotic stability for addressing fractional-order systems. To this end, a suitable controller that includes discontinuous terms is designed to guarantee the system states tends to zero asymptotically in a finite time when the system states do not admit stable performance. Moreover, the upper bound of the settling-time for finite-time stability is also estimated accurately. Finally, two numerical examples are presented to verify the correctness of the obtained stability results.