Abstract The fractional Laplacian,(−△) s, s∈(0, 1), appears in a wide range of physical
systems, including Lévy flights, some stochastic interfaces, and theoretical physics in …

An unsteady problem is considered for a space-fractional equation in a bounded domain. A
first-order evolutionary equation involves a fractional power of an elliptic operator of second …

A mathematical analysis is presented to establish the convergence of the matrix
transformation (or matrix transfer) method for the finite difference approximation of space …

In this article, we develop a fully discrete finite element method for the nonlinear Schrodinger
equation (NLS) with time-and space-fractional derivatives. The time-fractional derivative is …

This paper presents an efficient and concise double fast algorithm to solve high dimensional
time-space fractional diffusion problems with spectral fractional Laplacian. We first establish …

A convergence result is stated for the numerical solution of space-fractional diffusion
problems. For the spatial discretization, an arbitrary family of finite elements can be used …

Due to the successful applications in engineering, physics, biology, finance, etc., there has
been substantial interest in fractional diffusion equations over the past few decades, and …

A time dependent model problem with the Riesz or the Riemann-Liouville fractional
differential operator of order 1< α< 2 is considered. By penalyzing the primary variable of the …

Numerical solution of fractional order diffusion problems with homogeneous Dirichlet
boundary conditions is investigated on a square domain. An appropriate extension is …

This paper develops fast and accurate linear finite element method and fourth-order
compact difference method combined with matrix transfer technique to solve high …