Over the past few decades, there has been substantial interest in evolution equations that
involve a fractional-order derivative of order α∈(0, 1) in time, commonly known as …

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 …

We present a general framework for the rigorous numerical analysis of time-fractional
nonlinear parabolic partial differential equations, with a fractional derivative of order α∈(0,1) …

We develop proper correction formulas at the starting k-1 steps to restore the desired k th-
order convergence rate of the k-step BDF convolution quadrature for discretizing evolution …

We consider initial/boundary value problems for the subdiffusion and diffusion-wave
equations involving a Caputo fractional derivative in time. We develop two fully discrete …

We introduce a modified L1 scheme for solving time fractional partial differential equations
and obtain error estimates for smooth and nonsmooth initial data in both homogeneous and …

For the first time in literature, semi-implicit spectral approximations for nonlinear Caputo time-
and Riesz space-fractional diffusion equations with both smooth and non-smooth solutions …

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 …

In this work, we consider a time-fractional Allen–Cahn equation, where the conventional first
order time derivative is replaced by a Caputo fractional derivative with order α ∈ (0, 1) …

A survey is given of convergence results that have been proved when the L1 scheme is
used to approximate the Caputo time derivative Dα t (where 0< α< 1) in initial-boundary …