  Let $\mathcal{G}_{n, \beta^*}$ $(\mathcal{G}^*_{n,\beta^*})$ be the set of
all (connected) graphs of order $n$ with fractional matching number $\beta^*$.
In this paper, the graphs with maximal spectral radius in
$\mathcal{G}_{n,\beta^*}$ and $\mathcal{G}^*_{n,\beta^*}$ are characterized,
respectively. Moreover, a lower bound for the spectral radius in graphs with
order $n$ to guarantee the existence of a perfect fractional matching is also
given, which generalizes the main result of O [Suil O, Spectral radius and
matchings in graphs, Linear Algebra and its Applications, 2020].
