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 …

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 …

A Numerical solution of the Caputo-time and Riesz-space fractional reaction–diffusion
model is considered in this paper. Based on finite difference schemes, we formulate both …

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 …

Herein, we construct an explicit modal numerical solver based on the spec-tral Petrov–
Galerkin method via a specific combination of shifted Cheby-shev polynomial basis for …

This article proposes an efficient simulation to investigate the fractal-fractional (FF) pollution
model's solution behavior for a network of three lakes connected by channels. With the aid of …

‎ 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 …

Herein, we present an algorithm for handling fractional delay differential equations (FDDEs).
Chebyshev polynomials (CPs) class of the seventh kind is a subclass of the generalized …