  Let $q$ be an odd prime power. Let $F_1(x)=x^{d_1}$ and $F_2(x)=x^{d_2}$ be
power mappings over $\mathrm{GF}(q^2)$, where $d_1=q-1$ and
$d_2=d_1+\frac{q^2-1}{2}=\frac{(q-1)(q+3)}{2}$. In this paper, we study the the
boomerang uniformity of $F_1$ and $F_2$ via their differential properties. It
is shown that, the boomerang uniformity of $F_i$ ($i=1,2$) is 2 with some
conditions on $q$.
