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We consider the isogeometric analysis for fractional PDEs involving thefractional Laplacian in two dimensions. An isogeometric collocation method isdeveloped to discretize the fractional Laplacian and applied to the fractionalPoisson 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 withfinite element analysis shows that the method enjoys higher accuracy per degreeof freedom and has a better convergence rate. We demonstrate that isogeometricanalysis offers a novel and promising computational tool for nonlocal problems.

Isogeometric Collocation Method for the Fractional Laplacian in the 2D Bounded Domain