Mittag–Leffler stability and generalized Mittag–Leffler stability of fractional-order gene regulatory networks

Gene regulatory networks have attracted much attention, and the networks with integer-order have been well studied. Fractional-order gene regulatory networks have been shown that it is more suitable to model gene regulation mechanism, but has rarely been researched. In this paper, a class of fractional-order gene regulatory networks is studied. Some criteria on the Mittag–Leffler stability and generalized Mittag–Leffler stability are established by using the fractional Lyapunov method for these networks. The existence of the equilibrium point is also considered. One illustrative example is provided to show the effectives of the obtained results.