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 …

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 …

We develop direct solution techniques for solving high-order differential equations with
constant coefficients using the spectral tau method. The spatial approximation is based on …

Herein, we build and implement a combination of Lucas polynomials basis that fulfills the
spatial homogenous boundary conditions. This basis is then used to solve the time-fractional …

In this research, a compact combination of Chebyshev polynomials is created and used as a
spatial basis for the time fractional fourth-order Euler–Bernoulli pinned–pinned beam. The …

This paper presents a numerical strategy for solving the nonlinear time fractional Burgers's
equation (TFBE) to obtain approximate solutions of TFBE. During this procedure, the …

This article is dedicated to propose a spectral solution for the non-linear Fitzhugh–Nagumo
equation. The proposed solution is expressed as a double sum of basis functions that are …

‎ The main goal of this research work is to provide a numerical technique based on choosing
a set of basis functions for handling the third-order time-fractional Korteweg–De Vries …

The goal of this study is to suggest a new general triple integral transform known as Gamar
transform. Next, we compare the current transform to a number of existing triple integral …

This paper is devoted to the construction of certain polynomials related to Lucas
polynomials, namely, modified Lucas polynomials. The constructed modified Lucas …