Note on fractional difference Gronwall inequalities

摘要

This note is a reaction on a bunch of fractional inequalities that appeared in the last few years, and that are all based on what claims to be a fractional discrete Gronwall inequality. However, we show by a counterexample that this inequality is not correct. Stimulated by this, the main aim of this note is to propose new inequalities and illustrate the results on examples. Asymptotic properties of a solution of a linear equation are studied as well. Moreover, a brief discussion of other related results is given.