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 …

Fractional calculus, albeit a synonym of fractional integrals and derivatives which have two
main characteristics—singularity and nonlocality—has attracted increasing interest due to its …

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 …

In this paper, we analyze the spectra of the preconditioned matrices arising from discretized
multi-dimensional Riesz spatial fractional diffusion equations. The finite difference method is …

This paper is concerned with the construction and analysis of a novel linearized compact
ADI scheme for the two-dimensional Riesz space fractional nonlinear reaction–diffusion …

Starting with an introduction to fractional derivatives and numerical approximations, this
book presents finite difference methods for fractional differential equations, including time …

In this paper, a compact finite difference scheme is constructed and investigated for the
fourth‐order time‐fractional integro‐differential equation with a weakly singular kernel. In the …

In this work we study the finite difference method for the fractional diffusion equation with
high-dimensional hyper-singular integral fractional Laplacian. We first propose a simple and …

In the current paper, an error estimate has been proposed to find a second-order finite
difference scheme for solving the Riesz space distributed-order diffusion equation. The …