This paper presents a method for the approximate solution of the time-fractional nonlinear
sine-Gordon and the Klein-Gordon models described in Caputo sense and with the order 1< …

In this paper, we present a fully discrete and structure-preserving scheme for the nonlinear
fractional Schrödinger equations. The key is to introduce a scalar auxiliary variable and …

Efficient long-time integration of nonlinear fractional differential equations is significantly
challenging due to the integro-differential nature of the fractional operators. In addition, the …

In this paper, a three-dimensional time-dependent Riesz space-fractional diffusion equation
is considered, and an alternating direction implicit (ADI) difference scheme is proposed, in …

In this article, we introduce a local discontinuous Galerkin (LDG) method combined with the
generalized second-order backward difference formula with a shifted parameter θ (BDF2-θ) …

Fractional advection–dispersion equations (ADEs) appear to have great potential to predict
various non-Fickian dispersion processes as the anomalous transport in surface and …

Phase field models have been widely considered to simulate corrosion dynamics
characterised by moving boundaries. The benefits of using these models rely on the fact that …

In this paper, we study the nonlinear Riesz space-fractional convection–diffusion equation
over a finite domain in two dimensions with a reaction term. The Crank–Nicolson difference …

In this paper, with the help of the generalized Hopf-Cole transformation, we first convert the
nonhomogeneous Burgers' equation into an equivalent heat equation with the derivative …

Abstract Time–space fractional Fokker–Planck equations (TSFFPEs) are a class of very
useful models for describing some practical phenomena in statistical physics. In the present …