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We establish an integration by parts formula in bounded domains for thehigher order fractional Laplacian $(-\Delta)^s$ with $s>1$. We also obtain thePohozaev identity for this operator. Both identities involve local boundaryterms, and they extend the identities obtained by the authors in the case$s\in(0,1)$.  As an immediate consequence of these results, we obtain a unique continuationproperty for the eigenfunctions $(-\Delta)^s\phi=\lambda\phi$ in $\Omega$,$\phi\equiv0$ in $\mathbb R^n\setminus\Omega$.

Local integration by parts and Pohozaev identities for higher order fractional Laplacians