We introduce a class of orthogonal functions associated with integral and fractional
differential equations with a logarithmic kernel. These functions are generated by applying a …

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 work we study the finite difference method for the fractional diffusion equation with
high-dimensional hyper-singular integral fractional Laplacian. We first propose a simple and …

The usual classical polynomials-based spectral Galerkin and Petrov–Galerkin methods
enjoy high-order accuracy for problems with smooth solutions. However, their accuracy and …

In this article we investigate the regularity of the solution to the fractional diffusion, advection,
reaction equation on a bounded domain in R 1. The analysis is performed in the weighted …

A spectral Galerkin approximation of a optimal control problem governed by a fractional
advection–diffusion–reaction equation with integral fractional Laplacian is investigated in …

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 …

We present two new classes of orthogonal functions, log orthogonal functions and
generalized log orthogonal functions, which are constructed by applying a mapping to …

In this paper we investigate the numerical approximation of the fractional diffusion,
advection, reaction equation on a bounded interval. Recently the explicit form of the solution …

In this paper, we construct a dissipation-preserving difference scheme for two-dimensional
nonlinear generalized wave equations with the integral fractional Laplacian. We discuss the …