The positive definiteness of real quadratic forms with convolution structures plays an
important role in stability analysis for time-stepping schemes for nonlocal operators. In this …

In this paper, we derive the improved regularity for two-dimensional nonlinear time fractional
telegraph equations by virtue of the technic of decomposition at first. Then, the famous L 2-1 …

This paper introduces a novel temporal second-order fully discrete approach of finite
element method (FEM) and its fast two-grid FEM on non-uniform meshes, which aims to …

A novel discrete gradient structure of the variable-step fractional BDF2 formula
approximating the Caputo fractional derivative of order is constructed by a local-nonlocal …

In this paper, the multi-term time-space fractional diffusion equation with fractional boundary
conditions is considered. The fractional derivative in space is approximated by the standard …

A unified discrete gradient structure of the second order nonuniform integral averaged
approximations for the Caputo fractional derivative and the Riemann–Liouville fractional …

The complete positivity, ie, positivity of the resolvent kernels, for convolutional kernels is an
important property for the positivity property and asymptotic behaviors of Volterra equations …

In this paper, we develop a finite difference method for solving the wave equation with
fractional damping in 1D and 2D cases, where the fractional damping is given based on the …

Two temporal second-order energy stable schemes with variable time step sizes are
constructed for the time fractional Cahn–Hilliard model. Nonuniform L1+ formula is utilized …

This paper constructs and analyzes an α-robust and new two-grid finite element method
(FEM) with nonuniform L2-1 σ formula and its fast algorithms for nonlinear time-fractional …