  We study the Hausdorff dimension of the sets on which the pointwise
convergence of the solutions to the fractional Schr\"odinger equation
$e^{it(-\Delta)^\frac m2}f$ fails when $m\in(0,1)$ in one spatial dimension.
The pointwise convergence along a non-tangential curve and a set of lines are
also considered, where we find different nature from the case when
$m\in(1,\infty)$. In particular, non-tangential curves are no longer regarded
as vertical lines.
