In this review paper, we are mainly concerned with the finite difference methods, the
Galerkin finite element methods, and the spectral methods for fractional partial differential …

A one dimensional fractional diffusion model with the Riemann–Liouville fractional
derivative is studied. First, a second order discretization for this derivative is presented and …

Because of the nonlocal properties of fractional operators, higher order schemes play a
more important role in discretizing fractional derivatives than classical ones. The striking …

In this paper, the multi-term temporal fractional order and temporal distributed-order
parabolic equations with fractional Laplacian are numerically investigated. Several …

In this paper, we consider two types of space-time fractional diffusion equations (STFDE) on
a finite domain. The equation can be obtained from the standard diffusion equation by …

In this paper, we consider a two-sided space-fractional diffusion equation with variable
coefficients on a finite domain. Firstly, based on the nodal basis functions, we present a new …

We consider high order finite difference methods for two-dimensional fractional differential
equations with temporal Caputo and spatial Riemann-Liouville derivatives in this paper. We …

In this paper, we focus on fast solvers with linearithmic complexity in space for high-
dimensional time-fractional subdiffusion equations. Firstly, we present two alternating …

Second-order backward difference formula (BDF2) is considered for time approximation of
Riesz space-fractional diffusion equations. The Riesz space derivative is approximated by …

In this paper, we study Toeplitz-like linear systems arising from time-dependent one-
dimensional and two-dimensional Riesz space-fractional diffusion equations with variable …