Volterra subdiffusion problems with weakly singular kernel describe the dynamics of
subdiffusion processes well. The graded L 1 scheme is often chosen to discretize such …

In this paper, we study the variable-order (VO) time-fractional diffusion equations. For a VO
function α (t) ∈ (0, 1) α (t)∈(0, 1), we develop an exponential-sum-approximation (ESA) …

The $ p $-step backwards difference formula (BDF) for solving the system of ODEs can result
in a kind of all-at-once linear systems, which are solved via the parallel-in-time …

We develop a preconditioned fast divided-and-conquer finite element approximation for the
initial-boundary value problem of variable-order time-fractional diffusion equations. Due to …

We develop a fast divide-and-conquer indirect collocation method for the homogeneous
Dirichlet boundary value problem of variable-order space-fractional diffusion equations. Due …

In this paper, we propose a fast second-order approximation to the variable-order (VO)
Caputo fractional derivative, which is developed based on $ L2 $-$1 _\sigma $ formula and …

We develop a fast indirect collocation method for a two-sided variable-order space-fractional
diffusion equation, which models, eg, the superdiffusive transport of solute in a …

A robust fast method for mobile-immobile variable-order (VO) time-fractional diffusion
equations (tFDEs) is developed, superiorly handling the cases of small or vanishing lower …

We focus on a time-dependent one-dimensional space-fractional diffusion equation with
constant diffusion coefficients. An all-at-once rephrasing of the discretized problem, obtained …

A divide-and-conquer solver coupled with Tensor-Train (TT) format is proposed for solving
the d-dimensional time-space fractional diffusion equations with alternating direction implicit …