For any $k \in \mathbb{N}$, the $k$-subdivision of graph $G$ is a simple graph $G^{\frac{1}{k}}$, which is constructed by replacing each edge of $G$ with a path of length $k$. In [Moharram N. Iradmusa, On colorings of graph fractional powers, Discrete Math., (310) 2010, No. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $G$ has been introduced as a fractional power of $G$, denoted by $G^{\frac{m}{n}}$. In this regard, we investigate domination number and independent domination number of fractional powers of graphs.