  A {\it fractional matching} of a graph $G$ is a function $f$ giving each edge
a number in $[0,1]$ so that $\sum_{e\in \Gamma(v)}f(e)\leq 1$ for each $v\in
V(G)$, where $\Gamma(v)$ is the set of edges incident to $v$. The {\it
fractional matching number} of $G$, written $\alpha'_{*}(G)$, is the maximum of
$\sum_{e\in E(G)}f(e)$ over all fractional matchings $f$. In this paper, we
propose the relations between the fractional matching number and the signless
Laplacian spectral radius of a graph. As applications, we also give sufficient
spectral conditions for existence of a fractional perfect matching in a graph
in terms of the signless Laplacian spectral radius of the graph and its
complement.
