  In this work, we will give proper estimates for the discrete convolution
complementary (DCC) kernels, which leads to the asymptotically compatible
fractional Gr\"onwall inequality. The consequence can be applied in the
analysis of the stability and pointwise-in-time error of difference-type
schemes on a non-uniform mesh. The pointwise error is explicitly bound when a
non-uniform time grid is given by a specific scale function e.g. graded mesh,
can be given directly. Numerical experiments towards the conclusion of this
work validate the error analysis.
