Rigidity of minimizers in nonlocal phase transitions

We obtain the classification of certain global bounded solutions for semilinear nonlocal equations of the type $${\mathrm{△}}^{s}u=W^{\mathrm{\prime }}(u)$$ in ${\mathbb{R}}^n$,with $s\in (1\mathrm{/}2,1),$ where $W$ is a double well potential.