  Let $G$ be a graph with order $n$ and let $g, f : V (G)\rightarrow N$ such
that $g(v)\leq f(v)$ for all $v\in V(G)$. We say that $G$ has all fractional
$(g, f)$-factors if $G$ has a fractional $p$-factor for every $p: V
(G)\rightarrow N$ such that $g(v)\leq p(v)\leq f (v)$ for every $v\in V(G)$.
Let $a<b$ be two positive integers. %and $G$ \textbf{a graph} of order $n$
sufficiently large %for $a$ and $b$. If $g\equiv a$, $f\equiv b$ and $G$ has
all fractional $(g,f)$-factors, then we say that $G$ has all fractional
$[a,b]$-factors. Suppose that $n$ is sufficiently large for $a$ and $b$.
  This paper contains two results on the existence of all $(g,f)$-factors of
graphs. First, we derive from Anstee's fractional $(g,f)$-factor theorem a
similar characterization for the property of all fractional $(g,f)$-factors.
Second, we show that $G$ has all fractional $[a, b]$-factors if the minimum
degree is at least $\frac{1}{4a}((a+b-1)^2+4b)$ and every pair of nonadjacent
vertices has cardinality of the neighborhood union at least $bn/(a + b)$. These
lower bounds are sharp.
