In this work, we propose a Crank--Nicolson-type scheme with variable steps for the time
fractional Allen--Cahn equation. The proposed scheme is shown to be unconditionally …

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 …

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 …

The discrete gradient structure and the positive definiteness of discrete fractional integrals or
derivatives are fundamental to the numerical stability in long-time simulation of nonlinear …

In this paper, we study the problem of finding the solution of a multi-dimensional time
fractional reaction–diffusion equation with nonlinear source from the final value data. We …

This paper presents the fractional formulation and numerical solution of a non-linear
fractional diffusion equation with advection and reaction terms. The fractional derivative …

The purpose of this contribution is to present or implement generalized finite difference
method (GFDM) for the first time in order to solve the reaction convection Diffusion equation …

The solution of the nonlinear subdiffusion equation has the initial layer and its initial energy
may decay very fast. Therefore, it is important to investigate the evolution of the solution at …

We prove the existence and uniqueness of the solution to a variable-order fractional
stochastic differential equation driven by a multiplicative white noise, which describes the …

Stability and optimal convergence analysis of a non-uniform implicit-explicit L1 finite element
method (IMEX-L1-FEM) is studied for a class of time-fractional linear partial …