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 …

Since fractional derivatives are integrals with weakly singular kernel, the discretization on
the uniform mesh may lead to poor accuracy. The finite difference approximation of Caputo …

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 …

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 …

In this article, a class of two-dimensional Riesz space fractional diffusion equations is
considered. Some fractional spaces are established and some equivalences between …

New numerical techniques are presented for the solution of a two-dimensional anomalous
sub-diffusion equation with time fractional derivative. In these methods, standard central …

In this paper, we consider the numerical method for solving the two-dimensional fractional
diffusion-wave equation with a time fractional derivative of order α (1<α<2). A difference …