Variable-order (VO) fractional differential equations (FDEs) with a time (t), space (x) or other
variables dependent order have been successfully applied to investigate time and/or space …

Variable-order fractional operators were conceived and mathematically formalized only in
recent years. The possibility of formulating evolutionary governing equations has led to the …

In this paper we construct a new difference analog of the Caputo fractional derivative (called
the L 2-1 σ formula). The basic properties of this difference operator are investigated and on …

In this paper, compact finite difference schemes for the modified anomalous fractional sub-
diffusion equation and fractional diffusion-wave equation are studied. Schemes proposed …

In this paper, a compact finite difference scheme for the fractional sub-diffusion equations is
derived. After a transformation of the original problem, the L1 discretization is applied for the …

The cable equation plays a central role in many areas of electrophysiology and in modeling
neuronal dynamics. This paper reports an accurate spectral collocation method for solving …

Since fractional derivatives are integrals with weakly singular kernel, the discretization on
the uniform mesh may lead to poor accuracy. The finite difference approximation of Caputo …

Fractional derivatives hold memory effects, and they are extensively used in various real-
world applications. However, they also need large storage space and cause poor efficiency …

The aim of this paper is to develop an accurate discretization technique to solve a class of
variable-order fractional (VOF) reaction-diffusion problems. In the spatial direction, the …

While several high-order methods have been developed for fractional PDEs (FPDEs) with
fixed order, there are no such methods for FPDEs with field-variable order. These equations …