What is the explicit solution of $(-\Delta)^s u = \chi_{B}$ in $\mathbb{R}^N$ with $0< s<1$ and $\chi$ is the characteristic function? The answer should follow from the potential theory but I am not getting it in a simple form like the laplacian. Note that by known facts $u$ is continuous and radially symmetric.

What is the explicit solution of $(-\Delta)^s u = \chi_{B}$ in $\mathbb{R}^N$ with $0< s<1$ and $\chi$ is the characteristic function and $B$ is the unit ball around the origin? The answer should follow from the potential theory (answer follows by convolution theory) but I am not getting it in a simple form like the laplacian. Note that by known facts $u$ is continuous and radially symmetric.