In this paper, a generalized fractional $(q,h)$-Gronwall inequality is investigated. Based on this inequality, we derive the uniqueness theorem and the finite-time stability criterion of nonlinear fractional delay $(q,h)$-difference systems. Several examples are given to illustrate our theoretical result.

In this paper, we give a new method to show a monotonicity result for a function $f$ satisfying $(_{a}\nabla_{h}^{\nu}f)(t)\leq0$ ($(_{a}\nabla_{h,\ast}^{\nu}f)(t)\leq0$) with $\nu\in(0,1]$, which has never been solved in other papers. In addition, we give an example to illustrate one of our main results.