In this paper, an implicit robust difference method with graded meshes is constructed for the
modified Burgers model with nonlocal dynamic properties. The L1 formula on graded …

This work proposes a robust ADI scheme on graded mesh for solving three-dimensional
subdiffusion problems. The Caputo fractional derivative is discretized by L1 scheme, where …

In this paper, we consider an orthogonal spline collocation (OSC) method to solve the fourth-
order multi-term subdiffusion equation. The L1 method on graded meshes is employed in …

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 …

In this paper, we study the orthogonal Gauss collocation method (OGCM) with an arbitrary
polynomial degree for the numerical solution of a two-dimensional (2D) fourth-order …

This paper deals with the solution of the Kirchhoff parabolic equation involving the Caputo–
Fabrizio fractional derivative with non-singular kernel. We represent the mild solution by …

An initial-boundary value problem of the form D t α u+ Δ 2 u− c Δ u= f D_t^αu+\varDelta^2uc\
varDeltau=f is considered, where D t α D_t^α is a Caputo temporal derivative of order α∈(0 …

A time-fractional Allen-Cahn initial-boundary value problem is considered, where the
bounded spatial domain Ω lies in R d for some d∈{1, 2, 3} and has smooth boundary or is …

A distributed order time fractional diffusion equation whose solution has a weak singularity
near the initial time t= 0 t= 0 is considered. The numerical method of the paper uses the well …