In this note we give equivalent characterizations for a fractional Triebel-Lizorkin space \(F_{p,q}^s(\Omega)\) in terms of first-order differences in a uniform domain \(\Omega\). The characterization is valid for any positive, non-integer real smoothness \(s\in \mathbb{R}_+\setminus \mathbb{N}\) and indices \( 1 \leq p < \infty \), \(1\leq q \leq \infty\) as long as the fractional part \(s\) is greater than \(d/p-d/q\).