Fast alternating-direction finite difference methods for three-dimensional space-fractional diffusion equations

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fPINNs: Fractional Physics-Informed Neural Networks (2018, methodology): “In [36, 37, 38, 39], only the 3D extension of the Riesz space-fractional derivatives is considered, which differs from the directional fractional Laplacian of our interest; in [40], Riesz fractional Laplacian is first regularized by singularity subtraction and then approximated by using trapezoidal ”
A Crank-Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation (2014, methodology): “Some fast solution techniques were developed in [43, 44, 45, 40, 41] to solve the space fractional differential equations, in which the fractional derivative operators are discretized by the finite difference methods that yield a coefficient matrix with special structures.”
A Petrov–Galerkin finite element method for variable-coefficient fractional diffusion equations (2015, methodology): “A careful study needs to be carried out to investigate whether the stiffness matrix has certain Toeplitz-like structure as in the case of finite difference methods, so that a fast Fourier transform based fast Krylov subspace iterative method can be developed which has an almost linear computational ”