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 …

This article reviews convolution quadrature and its uses, extends the known approximation
results for the case of sectorial Laplace transforms to finite-part convolutions with non …

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 …

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

The subject of fractional calculus and its applications (that is, convolution-type pseudo-
differential operators including integrals and derivatives of any arbitrary real or complex …

It is well known that the trapezoidal rule converges geometrically when applied to analytic
functions on periodic intervals or the real line. The mathematics and history of this …

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) …

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 …

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 …