Fourier Transform of Fractional Laplacian

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I'm trying to solve a PDE with a spectral method.

The PDE has a fractional Laplacian... $\Delta^s$.

In regards to a numerical implementation, will the "s" term simply become the exponent of the "differentiation matrices".

$\widehat{(-\Delta)^s f}(\xi) = |\xi|^{2s} \hat f(\xi).$

Or is it not so simple?