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 the present work, first, a new fractional numerical differentiation formula (called the L1-2
formula) to approximate the Caputo fractional derivative of order α (0< α< 1) is developed. It …

A fast element-free Galerkin (EFG) method is proposed for the numerical analysis of the
fractional diffusion-wave equation. In this method, a fast time discrete scheme is first derived …

This paper reports a novel numerical technique for solving the time variable fractional order
mobile-immobile advection-dispersion (TVFO-MIAD) model with the Coimbra variable time …

In this paper, a meshless generalized finite difference method (GFDM) is proposed to solve
the time fractional diffusion-wave (TFDW) equations. A second-order temporal discretization …

In the current decade, the meshless methods have been developed for solving partial
differential equations. The meshless methods may be classified in two basic parts: 1. The …

ABSTRACT A novel numerical technique is considered for the solution of a multi-term time-
fractional diffusion equation. The orthogonal spline collocation method is used for in space …

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 …

We present the analytical formulation and the finite element solution of a fractional-order
nonlocal continuum model of a Euler-Bernoulli beam. Employing consistent definitions for …

This paper proposes the alternating direction implicit (ADI) numerical approaches for
computing the solution of multi-dimensional distributed-order fractional integrodifferential …