Finite difference approximations for two-sided space-fractional partial differential equations

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A Fast Finite Difference Method for Three-Dimensional Time-Dependent Space-Fractional Diffusion Equations with Fractional Derivative Boundary Conditions (2017, methodology): “We consider the three-dimensional time-dependent space-fractional PDE of order 1 < α, β, γ < 2 that is enclosed with the homogeneous Dirichlet and fractional derivative boundary conditions [1,19,20,31]”
Implicit difference approximation for the time fractional diffusion equation (2006, background): “Meerschaert et al. proposed finite difference approximations for two-sided space-fractional partial dierential equations [ 15 ] and fractional advection-dispersion flow equations [16].”
The homotopy analysis method for solving the time-fractional Fornberg-Whitham equation and comparison with Adomian's decomposition method (2013, methodology): “These methods include the finite difference method [4–6], the Adams–Bashforth–Moulton method [7], the homotopy perturbation method (HPM) [8–10], the generalized differential transform method [11,12], the variational iteration method [13–15] and the Adomian’s decomposition method (ADM) [16,17].”
Matrix approach to discrete fractional calculus II: Partial fractional differential equations (2008, methodology): “For two-sided space-fractional partial dierential equations the shifted Gr unwald-Letnikov formula was proposed and discussed in [ 41 ].”