The q-fractional analogue for Gronwall-type inequality

Abstract

In this article, we utilize \emph{q}--fractional Caputo initial value problems of order $0<\alpha \le 1$ to derive a \emph{q}--analogue for Gronwall--type inequality. Some particular cases are derived where \emph{q}--Mittag--Leffler functions and \emph{q}--exponential type functions are used. An example is given to illustrate the validity of the derived inequality.