q-Mittag-Leffler stability and Lyapunov direct method for differential systems with q-fractional order

Abstract

Abstract In this paper, using the theory of q-fractional calculus, we deal with the q-Mittag-Leffler stability of q-fractional differential systems, and based on it, we analyze the direct Lyapunov method of q-fractional differential systems. Several sufficient criteria are established to guarantee the q-Mittag-Leffler stability and asymptotic stability for the differential systems with q-fractional order.

Keywords

• q-fractional calculus
• q-Mittag-Leffler functions
• q-Mittag-Leffler stability
• Lyapunov method