  A fractional matching of a graph $G$ is a function $f$ giving each edge a
number in $[0,1]$ such that $\sum_{e\in\Gamma(v)}f(e)\leq1$ for each vertex
$v\in V(G)$, where $\Gamma(v)$ is the set of edges incident to $v$. The
fractional matching number of $G$, written $\alpha^{\prime}_*(G)$, is the
maximum value of $\sum_{e\in E(G)}f(e)$ over all fractional matchings. In this
paper, we investigate the relations between the fractional matching number and
the signless Laplacian spectral radius of a graph. Moreover, we give some
sufficient spectral conditions for the existence of a fractional perfect
matching.
