What is a way to implement the Fractional Laplacian with Mathematica?

How can we apply such implementation to numerically solve the problem

$$(-\Delta)^su = 1 \text{ in } B_1(0), \\ u = 0 \text{ in } \mathbb{R}^2 \setminus B_1(0), $$ where $B_1(0)$ is the unit disk centered at the origin?