<italic>q</italic>-Mittag-Leffler stability and Lyapunov direct method for differential systems with <italic>q</italic>-fractional order.

In this paper, using the theory of <italic>q</italic>-fractional calculus, we deal with the <italic>q</italic>-Mittag-Leffler stability of <italic>q</italic>-fractional differential systems, and based on it, we analyze the direct Lyapunov method of <italic>q</italic>-fractional differential systems. Several sufficient criteria are established to guarantee the <italic>q</italic>-Mittag-Leffler stability and asymptotic stability for the differential systems with <italic>q</italic>-fractional order. [ABSTRACT FROM AUTHOR]