By developing a unified approach based on integral representations, we establish sharp quantitative stability estimates for critical points of the fractional Sobolev inequalities induced by the embedding $\dot{H}^s({\mathbb R}^n) \hookrightarrow L^{2n \over n-2s}({\mathbb R}^n)$ in the whole range of $s \in (0,\frac{n}{2})$.