The purpose of this book is to present a self-contained and up-to-date survey of numerical
treatment for the so-called time-fractional diffusion model and their mathematical analysis …

An exponential type of convolution quadrature is proposed as a time-stepping method for
the nonlinear subdiffusion equation with bounded measurable initial data. The method …

The solution of fractional-order differential problems requires in the majority of cases the use
of some computational approach. In general, the numerical treatment of fractional differential …

In this work, we extend the fractional linear multistep methods in C. Lubich, SIAM J. Math.
Anal., 17 (1986), pp. 704--719 to the tempered fractional integral and derivative operators in …

In this paper, we develop and analyze a spectral-Galerkin method for solving subdiffusion
equations, which contain Caputo fractional derivatives with order ν∈(0,1). The basis …

In this paper, a new derived method is developed for a known numerical differential formula
of the Caputo fractional derivative of order γ ∈ (1, 2) γ∈(1, 2)(Li and Zeng in Numerical …

This article concerns second-order time discretization of subdiffusion equations with time-
dependent diffusion coefficients. High-order differentiability and regularity estimates are …

Fractional differential equations (FDEs) describe subdiffusion behavior of dynamical
systems. Their nonlocal structure requires taking into account the whole evolution history …

This paper is concerned with the unconditionally optimal H 1-error estimate of a fast second-
order scheme for solving nonlinear subdiffusion equations on the nonuniform mesh. We use …

In this paper we consider a sub-diffusion problem where the fractional time derivative is
approximated either by the L1 scheme or by Convolution Quadrature. We propose new …