Mittag-Leffler stability of random-order fractional nonlinear uncertain dynamic systems with impulsive effects

This paper investigates the Mittag-Leffler stability (MLS) of nonlinear uncertain dynamic systems (NUDSs) with impulsive effects involving the random-order fractional derivative (ROFD) under the fuzzy concept. The major tool used in this paper is Lyapunov’s direct method, which brings high efficiency in surveying the stability theory of dynamic systems. Some algebraic inequalities on the ROFD are established, which is necessary to study the MLS of NUDSs. Examples and simulations are also provided to demonstrate the effectiveness of the derived theoretical results.