This paper is concerned with establishing novel expressions that express the derivative of
any order of the orthogonal polynomials, namely, Chebyshev polynomials of the sixth kind in …

Simulation and numerical study for the blood ethanol concentration system (BECS) and the
Lotka-Volterra system, ie, predator-prey equations (PPEs)(both of fractional order in the …

The main goal of this paper is to develop a new formula of the fractional derivatives of the
shifted Chebyshev polynomials of the third kind. This new formula expresses approximately …

An efficient technique, called pseudo-Galerkin, is performed to approximate some types of
linear/nonlinear BVPs. The core of the performance process is the two well-known weighted …

This article is interested in presenting and implementing two new numerical algorithms for
solving multi-term fractional differential equations. The idea behind the proposed algorithms …

This paper is focused on performing a new method for solving linear and nonlinear higher-
order boundary value problems (HBVPs). This direct numerical method based on spectral …

A new numerical scheme based on the tau spectral method for solving the linear hyperbolic
telegraph type equation is presented and implemented. The derivation of this scheme is …

This paper is concerned with presenting and analyzing a new technique for solving time
fractional telegraph equation. This technique is based on applying the spectral Galerkin …

New modified shifted Chebyshev polynomials (MSCPs) have been constructed over the
interval [α, β]. These polynomials are utilized as basis functions with the application of the …

This paper is devoted to proposing numerical algorithms based on the use of the tau and
collocation procedures, two widely used spectral approaches for the numerical treatment of …