  A fractional matching of a graph $G$ is a function $f:E(G)\rightarrow [0, 1]$
such that for any $v\in V(G)$, $\sum_{e\in E_{G}(v)}f(e)\leq1$, where
$E_{G}(v)=\{e\in E(G): e~ \mbox{is incident with} ~v~\mbox{in}~G\}$.The
fractional matching number of $G$ is $\mu_{f}(G)=\mathrm{max}\{\sum_{e\in
E(G)}f(e):f$ is a fractional matching of $G\}$. Let $k\in (0,n)$ is an integer.
In this paper, we prove a tight lower bound of the spectral radius to guarantee
$\mu_{f}(G)>\frac{n-k}{2}$ in a graph with minimum degree $\delta,$ which
implies the result on the fractional perfect matching due to Fan et al.
[Discrete Math. 345 (2022) 112892].
  For a set $\{A, B, C, \ldots\}$ of graphs, an $\{A, B, C, \ldots\}$-factor of
a graph $G$ is defined to be a spanning subgraph of $G$ each component of which
is isomorphic to one of $\{A, B, C, \ldots\}$.We present a tight sufficient
condition in terms of the spectral radius for the existence of a $\{K_2,
\{C_k\}\}$-factor in a graph with minimum degree $\delta,$ where $k\geq 3$ is
an integer. Moreover, we also provide a tight spectral radius condition for the
existence of a $\{K_{1, 1}, K_{1, 2}, \ldots , K_{1, k}\}$-factor with $k\geq2$
in a graph with minimum degree $\delta,$ which generalizes the result of Miao
et al. [Discrete Appl. Math. 326 (2023) 17-32].
