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 …

This work proposes a robust ADI scheme on graded mesh for solving three-dimensional
subdiffusion problems. The Caputo fractional derivative is discretized by L1 scheme, where …

In this paper we intend to establish fast numerical approaches to solve a class of initial-
boundary problem of time-space fractional convection–diffusion equations. We present a …

This article proposes the fast L1 alternating direction implicit (ADI) finite difference and
compact difference schemes to solve the fractional telegraph equation in three-dimensional …

High-order compact exponential finite difference scheme for solving the time fractional
convection–diffusion reaction equation with variable coefficients is considered in this paper …

The fuzzy fractional differential equation explains more complex real-world phenomena than
the fractional differential equation does. Therefore, numerous techniques have been timely …

We develop an efficient multigrid method combined with a high-order compact (HOC) finite
difference scheme on nonuniform rectilinear grids for solving 3D diagonal anisotropic …

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 …

The variable-order (VO) fractional calculus can be seen as a natural extension of the
constant-order, which can be utilized in physical and biological applications. In this study …

In this paper, a new hybrid scheme based multiquadric radial basis function-generated finite
difference (RBF-FD) method with Shishkin nodes is proposed to solve stationary convection …