Some remarks on the Gronwall integral inequality

Abstract

In this paper, a generalized Volterra‐type integral inequality is developed. On the basis of this inequality, the effect of fractional‐order ω$$ \omega $$ on the application of the integer‐order Gronwall integral inequality (IOGII) is discussed. Specially speaking, the IOGII cannot be directly used to reckon the solution of integral inequality with the order 0<ω<1$$ 0&amp;amp;lt;\omega &amp;amp;lt;1 $$. It seems that both the IOGII and the generalized Volterra‐type integral inequality can be applied to estimate the solution of integral inequality with the order ω≥1$$ \omega \ge 1 $$, and results are consistent, but this is just a coincidence.