This research apparatuses an approximate spectral method for the nonlinear time-fractional
partial integro-differential equation with a weakly singular kernel (TFPIDE). The main idea of …

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 …

The time-fractional diffusion equation is applied to a wide range of practical applications. We
suggest using a potent spectral approach to solve this equation. These techniques' main …

The basic aim of this paper is to develop new numerical algorithms for solving some linear
and nonlinear fractional-order differential equations. We have developed a new type of …

Through the current article, a numerical technique to obtain an approximate solution of one-
dimensional linear hyperbolic partial differential equations is implemented. A certain …

In this paper, our target is to implement and analyze numerical algorithms for the numerical
solutions of initial and boundary third-order singular-type equations, and in particular 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 …

Herein, we propose new efficient spectral algorithms for handling the fractional diffusion
wave equation (FDWE) and fractional diffusion wave equation with damping (FDWED). In …

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 …