Finite-time stability of discrete fractional delay systems: Gronwall inequality and stability criterion

•A generalized Gronwall inequality is given on finite time domain.•Finite-time stability of discrete fractional delay systems is discussed.•New finite-time stability criterion is provided. This study investigates finite-time stability of Caputo delta fractional difference equations. A generalized Gronwall inequality is given on a finite time domain. A finite-time stability criterion is proposed for fractional differential equations. Then the idea is extended to the discrete fractional case. A linear fractional difference equation with constant delays is considered and finite-time stable conditions are provided. One example is numerically illustrated to support the theoretical result.