are enough to establish unique continuation, in the fractional case they provide unique continuation only for the extended local problem and not for the fractional one. Such difficulty was overcome in [@FF] for the fractional Laplacian $(-\Delta)^{s}$ with $s\in(0,1)$, by a fine blow-up analysis and a precise classification of the possible blow-up limit profiles in terms of a Neumann eigenvalue problem on the half-sphere.

The problem of unique continuation for fractional laplacians with power $s\in(0,1)$ was also studied in [@Ruland] in presence of rough potentials using Carleman estimates and in [@Yu] for fractional operators with variable coefficients using an Almgren type monotonicity formula. As far as higher fractional powers of the laplacian, the main contribution to the problem of unique continuation is due to Seo in papers [@seo0; @seo1; @seo2], through Carleman inequalities; in particular papers [@seo0; @seo1; @seo2] consider fractional Schrödinger operators with potentials in Morrey spaces and prove a *weak* unique continuation result, i.e. vanishing of solutions which are zero on an open set; we recall that the *strong* unique continuation property instead requires the weaker assumption of infinite vanishing order at some point.

We observe that the presence of a coupling Neumann term in system produces substancial 