In this review paper, we are mainly concerned with the finite difference methods, the
Galerkin finite element methods, and the spectral methods for fractional partial differential …

In this paper, a fast linearized conservative finite element method is studied for solving the
strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme …

In this paper, a linearized L1-Galerkin finite element method is proposed to solve the
multidimensional nonlinear time-fractional Schrödinger equation. In terms of a temporal …

Current discretizations of variable-order fractional (V-OF) differential equations lead to
numerical solutions of low order of accuracy. This paper explores a high order numerical …

In this paper, we investigate distinct novel analytical and semi-analytical solutions of the
higher-order nonlinear Schrödinger equation with the non-Kerr nonlinear term by the …

Starting with the asymptotic expansion of the error equation of the shifted Grünwald–
Letnikov formula, we derive a new modified weighted shifted Grünwald–Letnikov (WSGL) …

As a natural generalization of the fractional Schrödinger equation, the variable-order
fractional Schrödinger equation has been exploited to study fractional quantum phenomena …

In this paper, a class of nonlinear Riesz space-fractional Schrödinger equations are
considered. Based on the standard Galerkin finite element method in space and Crank …

This paper is concerned with unconditionally optimal error estimates of linearized Galerkin
finite element methods to numerically solve some multi-dimensional fractional reaction …

In this manuscript, we consider an initial-boundary-value problem governed by a (1+ 1)-
dimensional hyperbolic partial differential equation with constant damping that generalizes …