In this review paper, we are mainly concerned with the numerical methods for solving
fractional equations, which are divided into the fractional differential equations (FDEs), time …

This work aims to provide a new Galerkin algorithm for solving the fractional Rayleigh-
Stokes equation (FRSE). We select the basis functions for the Galerkin technique to be …

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 …

The current manuscript introduces a novel numerical treatment for multi-term fractional
differential equations with variable coefficients. The spectral Galerkin approach is developed …

This paper is concerned with the application of the spectral tau and collocation methods to
delay multi-order fractional differential equations with vanishing delay rx (0< r< 1). The …

In this article, we propose two numerical schemes for solving the time-fractional heat
equation (TFHE). The proposed methods are based on applying the collocation and tau …

An open problem in the numerical analysis of spectral methods for fractional differential
equations is how to maintain the high-order accuracy for non-smooth solutions. The limited …

The main aim of this paper is to introduce a new class of orthogonal polynomials that
generalizes the class of Chebyshev polynomials of the first kind. Some basic properties of …

In this paper, we study and present a spectral numerical technique for solving a general
class of multi-order fractional pantograph equations with varying coefficients and systems of …

The paper presents a numerical simulation of the propagation characteristics of symmetric E-
type and H-type waves in microwave circular shielded waveguide with radially …