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 …

The principal aim of the current paper is to present and analyze two new spectral algorithms
for solving some types of linear and nonlinear fractional-order differential equations. The …

This paper presents an explicit formula that approximates the fractional derivatives of
Chebyshev polynomials of the first-kind in the Caputo sense. The new expression is given in …

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 …

This article is devoted to deriving a new linearization formula of a class for Jacobi
polynomials that generalizes the third‐kind Chebyshev polynomials class. In fact, this new …

This paper is dedicated to deriving novel formulae for the high‐order derivatives of
Chebyshev polynomials of the fifth‐kind. The high‐order derivatives of these polynomials …

In this paper a novel operational matrix of derivatives of certain basis of Legendre
polynomials is established. We show that this matrix is expressed in terms of the harmonic …

A general procedure to determine collocation methods for high order boundary value
problems is presented. These methods provide globally continuous differentiable solution in …

In this article, we propose new spectral solutions for odd-order two-point boundary value
problems. A numerical algorithm based on the use of collocation methods is implemented …

This chapter is concerned with analyzing and presenting some algorithms for treating some
kinds of fractional differential equations (FDEs) based on utilizing some suitable spectral …