A unified Petrov-Galerkin spectral method for fractional PDEs

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A review of operational matrices and spectral techniques for fractional calculus (2015, methodology): “Spectral methods can be classified into three types, namely the collocation [48–52], tau [53–56] and Galerkin [57–59] methods.”
An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data (2017, unknown): “1) are sufficiently smooth, for example u ∈ C2[0, T ], there are many time discretisation schemes in the literature, for example, Lubich’s fractional multistep methods [7], [30], [55], [65], [61], [62], [64], the L1 scheme and its modification [28], [26], [18], [29], [47], the spectral method [58] [”
Time two-mesh algorithm combined with finite element method for time fractional water wave model (2018, unknown): “In view of the difficulty for solving the analytic solutions, increasing scholars have started to study some effective numerical methods for solving complex FPDEs with time, space and space-time fractional derivatives, which include finite difference methods [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1”