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 …

A reaction-diffusion problem with a Caputo time derivative of order α∈(0,1) is considered.
The solution of such a problem is shown in general to have a weak singularity near the initial …

Stability and convergence of the L1 formula on nonuniform time grids are studied for solving
linear reaction-subdiffusion equations with the Caputo derivative. A discrete fractional …

Fractional differential equations (FDES), ie, differential equations involving fractional-order
derivatives, have received much recent attention in engineering, physics, biology and …

An initial-boundary value problem with a Caputo time derivative of fractional order $\alpha\in
(0, 1) $ is considered, solutions of which typically exhibit a singular behaviour at an initial …

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 present three schemes for the numerical approximation of fractional diffusion, which
build on different definitions of such a non-local process. The first method is a PDE approach …

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 …