A Fast Finite Difference Method for Three-Dimensional Time-Dependent Space-Fractional Diffusion Equations with Fractional Derivative Boundary Conditions

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fPINNs: Fractional Physics-Informed Neural Networks (2018, methodology): “In [24, 47, 48, 53], only the 3D extension of the Riesz spacefractional derivatives is considered, which differs from the directional fractional Laplacian of our interest; in [28], Riesz fractional Laplacian is first regularized by singularity subtraction and then approximated by using the trapezoid”
A Simple Solver for the Fractional Laplacian in Multiple Dimensions (2018, methodology): “…and fast preconditioners based on multigrid, but their scheme uses the so-called “coordinate fractional Laplacian” that takes a tensor product of one-dimensional operators and is not equivalent to (1) (see also related ﬁnite-diﬀerence approaches with diﬀerent operators [36,37,51,58]).”