We introduce a sampling-based machine learning approach, Monte Carlo fractional physics-
informed neural networks (MC-fPINNs), for solving forward and inverse fractional partial …

We propose two preconditioners based on the fast sine transformation for solving linear
systems with ill-conditioned multilevel Toeplitz structure. These matrices are generated by …

In this paper, a backward problem for a time–space fractional diffusion equation is
considered, which is to determine the initial data from a noisy final data. To deal with this ill …

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 …

In this paper, finite difference schemes for solving time-space fractional diffusion equations
in one dimension and two dimensions are proposed. The temporal derivative is in the …

An efficient finite difference method for the multi-dimensional differential equation with
variable-order Riemann-Liouville derivative is studied. Firstly, we construct an efficient …

In this paper, we develop two fast implicit difference schemes for solving a class of variable‐
coefficient time–space fractional diffusion equations with integral fractional Laplacian (IFL) …

In this paper, we develop a conditional Monte Carlo method for solving PDEs involving an
integral fractional Laplacian on any bounded domain in arbitrary dimensions. We first …

This study aims to investigate some theoretical results, numerical study and a real-word
application of the SFGLE, involving the fractional Laplacian. First, we describe the …

We provide the convergence analysis for a-Galerkin method to solve the fractional Dirichlet
problem. This can be understood as a follow-up of [H. Antil, P. Dondl, and L. Striet, SIAM J …