Erratum to: On stable manifolds for fractional differential equations in high-dimensional spaces

1 Erratum to: Nonlinear Dyn DOI 10.1007/s11071-016-3002-z

The second part of the statement in Proposition 9 of the original publication was incorrect. It should read as follows:

(ii) If $\xi (t)=(\xi ^{u}(t),\xi ^{s}(t))^{\hbox {T}}$ is a fixed point of $\mathcal {T}_{x^{s}}$ for some $x^{s}\in \mathbb {R}^{d^{s}}$ and $\left\| \xi \right\| _\infty \le r^{*}$, where $r^{*}$ satisfies (12), then $\xi (t)$ is a solution of (8) with $\xi ^{s}(0)=x^{s}$ and $\lim _{t\rightarrow \infty } \xi (t)=0$.