The \(q\)-fractional analogue for Gronwall-type inequality (Q2443728)

Summary: We utilize \(q\)-fractional Caputo initial value problems of order \(0 < \alpha < 1\) to derive a \(q\)-analogue for Gronwall-type inequality. Some particular cases are derived where \(q\)-Mittag-Leffler functions and \(q\)-exponential type functions are used. An example is given to illustrate the validity of the derived inequality.