Abstract
This paper investigates the asymptotical stability of Riemann-Liouville q-fractional neutral systems with mixed delays (constant time delay and distributed delay). By constructing some appropriate Lyapunov-Kravsovskii functionals, some sufficient conditions on delay-dependent and delay-independent asymptotical stability are obtained in terms of linear matrix inequality (LMI). Our employed method is based on the direct calculation of quantum derivatives of the Lyapunov-Kravsovskii functionals. Finally, two examples are presented to demonstrate the availability of our obtained results.