Pointwise convergence along a tangential curve for the fractional Schr\"odinger equation

In this paper we study the pointwise convergence problem along a tangential curve for the fractional Schr"odinger equations in one spatial dimension and estimate the capacitary dimension of the divergence set. We extend a prior paper by Lee and the first author for the classical Schr"odinger equation, which in itself contains a result due to Lee, Vargas and the first author, to the fractional Schr"odinger equation. The proof is based on a decomposition argument without time localization, which has recently been introduced by the second author.