Finite-time stability of linear fractional time-delay <italic>q</italic>-difference dynamical system.

In this paper, the finite-time stability of a class of fractional <italic>q</italic>-difference equations with time-delay is investigated. First, we state and prove a generalized <italic>q</italic>-Gronwall inequality. In addition, we introduce a delayed <italic>q</italic>-Mittag-Leffler type matrix function and explore explicit formula of solutions to the considered system. Then two criteria to guarantee finite-time stability are obtained by utilizing the proposed delayed <italic>q</italic>-Mittag-Leffler type matrix and generalized <italic>q</italic>-Gronwall inequality, respectively. Finally, an example and its simulation are presented to illustrate our main results. [ABSTRACT FROM AUTHOR]