In this review paper, the finite difference methods (FDMs) for the fractional differential
equations are displayed. The considered equations mainly include the fractional kinetic …

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 …

Fractional calculus, which has two main features—singularity and nonlocality from its origin—
means integration and differentiation of any positive real order or even complex order. It has …

The computational work and storage of numerically solving the time fractional PDEs are
generally huge for the traditional direct methods since they require total memory and work …

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the
two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed …

In this paper, we propose and analyze an efficient operational formulation of spectral tau
method for multi-term time–space fractional differential equation with Dirichlet boundary …

In this paper, two finite difference/element approaches for the time-fractional subdiffusion
equation with Dirichlet boundary conditions are developed, in which the time direction is …

Fractional differential equations are becoming increasingly used as a powerful modelling
approach for understanding the many aspects of nonlocality and spatial heterogeneity …

This paper develops a novel boundary meshless approach, Laplace transformed boundary
particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It …

The implicit finite difference scheme with the shifted Grünwald formula, which is
unconditionally stable, is employed to discretize fractional diffusion equations. The resulting …