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This paper shows $$ \sup_{f\in H^s(\mathbb{R}^n)}\dim_H\left\{x\in\mathbb{R}^n:\ \lim_{t\rightarrow0}e^{it(-\Delta)^\alpha}f(x)\neqf(x)\right\}\leq n+1-\frac{2(n+1)s}{n}\ \ \text{under}\ \ \begin{cases}n\geq2;\\ \alpha>\frac12;  \frac{n}{2(n+1)}<s\leq\frac{n}{2} . \end{cases} $$

An Upbound of Hausdorff's Dimension of the Divergence Set of the fractional Schr\"odinger Operator on $H^s(\mathbb R^n)