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 paper, we address the time-fractional heat conduction equation in one
spatial dimension, subject to nonlocal conditions in the temporal domain. To tackle this …

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 …

In this work, first, a family of fourth‐order methods is proposed to solve nonlinear equations.
The methods satisfy the Kung‐Traub optimality conjecture. By developing the methods into …

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 study utilizes a spectral tau method to acquire an accurate numerical solution of the
time-fractional diffusion equation. The central point of this approach is to use double basis …

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 focus of this investigation centers on the formulation of a novel spectral method
deployed to numerically solve partial integro-differential equations that possess memory …