Abstract The Spectral Finite Element Technique (SFEM) has Several Applications in the
Sciences, Engineering, and Mathematics, which will be Covered in this Review Article. The …

In this article, we will discuss the applications of the Spectral element method (SEM) and
Finite element Method (FEM) for fractional calculusThe so-called fractional Spectral element …

In this manuscript, we develop and analyze two high‐order schemes, CFD g− σ _ g-σ and
PQS g− σ _ g-σ, for generalized variable coefficients fractional reaction–diffusion equations …

This research aims to estimate the solutions of fractional-order partial differential equations
of spacial fractional and both time-space fractional order. For this, we use finite differences …

In this paper, we propose two new approximation methods on a general mesh for the
generalized Caputo fractional derivative of order α∈(0, 1). The accuracy of these two …

In this paper, an approximate method combining the finite difference and collocation
methods is studied to solve the generalized fractional diffusion equation (GFDE). The …

In this paper, the numerical method for solving a class of generalized fractional advection-
diffusion equation (GFADE) is considered. The fractional derivative involving scale and …

The current study is conducted to evaluate the numerical solution of the space-time
fractional Klein-Gordon equation. This equation is obtained by adopting the generalized …

Purpose This paper aims to present a high-order scheme to approximate generalized
derivative of Caputo type for μ∈(0, 1). The scheme is used to find the numerical solution of …

In this paper, a numerical scheme based on a general temporal mesh is constructed for a
generalized time-fractional diffusion problem of order α. The main idea involves the …