A new spectral method based on two classes of hat functions for solving systems of fractional differential equations and an application to respiratory syncytial virus infection

TL;DR

This paper introduces a spectral method using hat functions for efficiently solving systems of fractional differential equations, demonstrated through tests and an epidemiological application to respiratory syncytial virus infection.

Contribution

A novel spectral method based on two classes of hat functions for fractional differential equations, reducing computational effort and applicable to epidemiological models.

Findings

Method requires few computational resources.

High accuracy demonstrated on test problems.

Effective application to a respiratory virus model.

Abstract

We propose a new spectral method, based on two classes of hat functions, for solving systems of fractional differential equations. The fractional derivative is considered in the Caputo sense. Properties of the basis functions, Caputo derivatives, and Riemann-Liouville fractional integrals, are used to reduce the main problem to a system of nonlinear algebraic equations. By analyzing in detail the resulting system, we show that the method needs few computational efforts. Two test problems are considered to illustrate the efficiency and accuracy of the proposed method. Finally, an application to a recent mathematical model in epidemiology is given, precisely to a system of fractional differential equations modeling the respiratory syncytial virus infection.