  We consider the isogeometric analysis for fractional PDEs involving the
fractional Laplacian in two dimensions. An isogeometric collocation method is
developed to discretize the fractional Laplacian and applied to the fractional
Poisson problem and the time-dependent fractional porous media equation.
Numerical studies exhibit monotonous convergence with a rate of
$\mathcal{O}(N^{-1})$, where $N$ is the degrees of freedom. A comparison with
finite element analysis shows that the method enjoys higher accuracy per degree
of freedom and has a better convergence rate. We demonstrate that isogeometric
analysis offers a novel and promising computational tool for nonlocal problems.
