Some remarks on the Gronwall integral inequality

In this paper, a generalized Volterra-type integral inequality is developed. On the basis of this inequality, the effect of fractional-order $\omega$ 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 . 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 $\omega \ge 1$, and results are consistent, but this is just a coincidence.