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 work, we present an analysis based on a combination of the Laplace transform and
homotopy methods in order to provide a new analytical approximated solutions of the …

In this article, we present an efficient numerical algorithm, which combines the fourth-order
compact difference scheme (CDS) in space with the fast time two-mesh (TT-M) FBN-θ …

This work presents the homotopy perturbation transform method for nonlinear fractional
partial differential equations of the Caputo-Fabrizio fractional operator. Perturbative …

In this paper, we propose a numerical method for the solution of time fractional nonlinear
sine-Gordon equation that appears extensively in classical lattice dynamics in the continuum …

This paper mainly presents numerical solutions to an initial-boundary value problem of the
time-fractional Klein-Gordon equations. We developed a numerical scheme with the help of …

This article provides numerical simulations of the time-fractional coupled Korteweg–de Vries
and Klein–Gordon equations via the local meshless collocation method (LMCM) utilising the …

This paper is devoted to develo** spectral solutions for the nonlinear fractional Klein–
Gordon equation. The typical collocation method and the tau method are employed for …

An efficient numerical technique is proposed to solve one-and two-dimensional space
fractional tempered fractional diffusion-wave equations. The space fractional is based on the …

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< …