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 …

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) …

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, a complete error analysis is presented for fully discrete solutions of the
subdiffusion equation with a time-dependent diffusion coefficient, obtained by the Galerkin …

A proof of convergence is given for semi-and full discretizations of mean curvature flow of
closed two-dimensional surfaces. The numerical method proposed and studied here …

In this work, we establish the maximal ℓ^ p ℓ p-regularity for several time step** schemes
for a fractional evolution model, which involves a fractional derivative of order α ∈ (0, 2) …

Variable-exponent fractional models attract increasing attentions in various applications,
while the rigorous analysis is far from well developed. This work provides general tools to …

We propose a local modification of the standard subdiffusion model by introducing the initial
Fickian diffusion, which results in a multiscale diffusion model. The developed model …

For the Landau–Lifshitz–Gilbert (LLG) equation of micromagnetics we study linearly implicit
backward difference formula (BDF) time discretizations up to order $5 $ combined with …

It is shown that for a parabolic problem with maximal L^p-regularity (for 1<p<∞), the time
discretization by a linear multistep method or Runge--Kutta method has maximal ℓ^p …