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edited title

Explicit formula for spectral fractional Laplacian of power-function $(-\Delta)^s x^{\alpha}$ in $(0,1) \subset \mathbb R$

How can one compute the Neumann spectral fractional Laplacian of power function, $(-\Delta)^s x^{\alpha}$, with $\alpha >0$, in an interval $(0,1)$. I'm only aware of the formula in the whole space.