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 book provides efficient and reliable numerical methods for solving fractional calculus
problems. It focuses on numerical techniques for fractional integrals, derivatives, and …

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

This article aims to fill in the gap of the second-order accurate schemes for the time-
fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are …

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, an efficient and accurate spectral numerical method is presented for solving
second-, fourth-order fractional diffusion-wave equations and fractional wave equations with …

The fractional Fokker--Planck equation is an important physical model for simulating
anomalous diffusions with external forces. Because of the nonlocal property of the fractional …

The method of approximate particular solutions (MAPS) is an alternative radial basis
function (RBF) meshless method, which is defined in terms of a linear combination of the …