Tempered fractional-order models open up new possibilities for robust mathematical
modeling of complex multi-scale problems and anomalous transport phenomena. The …

Two difference schemes are derived for both one-dimensional and two-dimensional
distributed-order differential equations. It is proved that the schemes are unconditionally …

An all-at-once system of nonlinear algebra equations arising from the nonlinear tempered
fractional diffusion equation with variable coefficients is studied. Firstly, both the nonlinear …

Anomalous diffusion is often modelled in terms of the subdiffusion equation, which can
involve a weakly singular source term. For this case, many predominant time-step** …

Based on the superconvergent approximation at some point (depending on the fractional
order α, but not belonging to the mesh points) for Grünwald discretization to fractional …

In this paper, we study the following time-fractional Feynman-Kac equation-Δ G (x, t)= f (x,
t),~~~ 0< α< 1,~~ σ> 0. σ CD t α G (x, t)-Δ G (x, t)= f (x, t), 0< α< 1, σ> 0. As is well known, the …

This chapter is to introduce the normal and anomalous stochastic processes in physics. We
first briefly discuss normal Gaussian diffusion, that is, Brownian motion, which has …

We investigate a fast finite element scheme to a hidden-memory variable-order time-
fractional diffusion equation. Different from the traditional L1 methods, a fast approximation …

Anomalous and non-ergodic diffusion is ubiquitous in the natural world. Fractional Feynman-
Kac equations are used to characterize the functional distribution of the trajectories of the …

Power-law probability density function (PDF) plays a key role in both subdiffusion and Lévy
flights. However, sometimes because of the finiteness of the lifespan of the particles or the …