The numerical solutions for nonlinear fractional Gardner and Cahn‐Hilliard equations
arising in fluids flow are obtained with the aid of two novel techniques, namely, fractional …

For the first time in literature, semi-implicit spectral approximations for nonlinear Caputo time-
and Riesz space-fractional diffusion equations with both smooth and non-smooth solutions …

Recently there has been a growing interest in designing efficient numerical methods for the
solution of fractional differential equations. The solutions of such equations in general …

This paper develops and analyses a finite difference/spectral-Galerkin scheme for the
nonlinear fractional Schrödinger equations with Riesz space-and Caputo time-fractional …

Since the emergence of numerical methods in mathematical modeling, fundamental
properties such as convergence, efficiency, computational accuracy, and stability have been …

In this paper, we numerically investigate the space fractional nonlinear damped wave
equation. We construct a novel high-accuracy dissipation-preserving finite difference …

In this work, we consider a damped hyperbolic partial differential equation in multiple spatial
dimensions with spatial partial derivatives of non-integer order. The equation under …

Naturally preserving dissipative or conservative structures of a given continuous system in
discrete analogs is of high demand when designing numerical schemes for dissipative or …

This paper aims to develop a linearly implicit structure-preserving numerical scheme for the
space fractional sine-Gordon equation, which is based on the newly developed invariant …

In this paper, we devise an efficient dissipation-preserving fourth-order difference solver for
the fractional-in-space nonlinear wave equations. First of all, we present a detailed …