  Let $G$ be a graph and $h: E(G)\rightarrow [0,1]$ be a function. For any two
positive integers $a$ and $b$ with $a\leq b$, a fractional $[a,b]$-factor of
$G$ with the indicator function $h$ is a spanning subgraph with vertex set
$V(G)$ and edge set $E_h$ such that $a\leq\sum_{e\in E_{G}(v)}h(e)\leq b$ for
any vertex $v\in V(G)$, where $E_h = \{e\in E(G)|h(e)>0\}$ and $E_{G}(v)=\{e\in
E(G)| e~\mbox{is incident with}~v~\mbox{in}~G\}$. A graph $G$ is
ID-factor-critical if for every independent set $I$ of $G$ whose size has the
same parity as $|V(G)|$, $G-I$ has a perfect matching. In this paper, we
present a tight sufficient condition based on the spectral radius for a graph
to contain a fractional $[a,b]$-factor, which extends the result of Wei and
Zhang [Discrete Math. 346 (2023) 113269]. Furthermore, we also prove a tight
sufficient condition in terms of the spectral radius for a graph with minimum
degree $\delta$ to be ID-factor-critical.
