Henry-Gronwall Typeq-Fractional Integral Inequalities

Abstract

The study ofq-difference equations has gained intensive interest in the last years. It has been shown that these types of equations have numerous applications in diverse fields and thus have evolved into multidisciplinary subjects. In this paper, theq-fractional integral inequalities of Henry-Gronwall type are presented. By using inequality technique related to the quantum calculus, such integral inequalities are suggested. Furthermore, an applications toq-fractional integral equations is also given.