Convolution quadrature time discretization of fractional diffusion-wave equations

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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] [”
Numerical methods for time-fractional evolution equations with nonsmooth data: A concise overview (2018, methodology): “However, it generally only exhibits a first-order accuracy when solving fractional evolution equations even for smooth v and f [87, 83], since the requisite compatibility condition is usually not satisfied.”
The Poisson distribution, abstract fractional difference equations, and stability (2017, methodology): “These abstract fractional models, with unbounded operators, are closely connected with numerical methods for integro-differential equations [16, 41] and evolution equations with memory [35].”
The Exponentially Convergent Trapezoidal Rule (2014, background): “3), and applications to wave equations are described in [15, 16, 33].”
Regularity of solutions to a time-fractional diffusion equation (2010, methodology): “Note that ν = 1−α in the notation of [1], whereas ν = 1+α in the notation of [9].”