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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$E_{G}(v)=\{e\in E(G): e~ \mbox{is incident with} ~v~\mbox{in}~G\}$.Thefractional matching number of $G$ is $\mu_{f}(G)=\mathrm{max}\{\sum_{e\inE(G)}f(e):f$ 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 $\delta,$ whichimplies 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 ofa graph $G$ is defined to be a spanning subgraph of $G$ each component of whichis isomorphic to one of $\{A, B, C, \ldots\}$.We present a tight sufficientcondition in terms of the spectral radius for the existence of a $\{K_2,\{C_k\}\}$-factor in a graph with minimum degree $\delta,$ where $k\geq 3$ isan integer. Moreover, we also provide a tight spectral radius condition for theexistence 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 Miaoet al. [Discrete Appl. Math. 326 (2023) 17-32].

Fractional matching, factors and spectral radius in graphs involving minimum degree