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 …

This article devotes to developing robust and simple correction techniques with efficient
algorithms for a class of second-order time stepping methods, namely the shifted fractional …

We investigate a second-order accurate time-stepping scheme for solving a time-fractional
diffusion equation with a Caputo derivative of order\(\alpha\in (0, 1)\). The basic idea of our …

In this work, two Crank–Nicolson schemes without corrections are developed for sub-
diffusion equations. First, we propose a Crank–Nicolson scheme without correction for …

Thanks to the singularity of the solution of linear subdiffusion problems, most time-stepping
methods on uniform meshes can result in O (τ) accuracy where τ denotes the time step. The …

An exponential-type function was discovered to transform known difference formulas by
involving a shifted parameter θ to approximate fractional calculus operators. In contrast to …

In recent years, the numerical theory of fractional models has received more and more
attention from researchers, due to the broad and important applications in materials and …

Time-fractional reaction-diffusion (TFRD) equation is an important fractional parabolic
equation, and the research of its numerical solution has scientific significance and …

A general conversion strategy by involving a shifted parameter $\theta $ is proposed to
construct high-order accuracy difference formulas for fractional calculus operators. By …