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Vieta–Lucas wavelets method for fractional linear and nonlinear delay differential equations

Shafaq Idrees (Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan)
Umer Saeed (NUST Institute of Civil Engineering, School of Civil and Environmental Engineering, National University of Sciences and Technology (NUST), Islamabad, Pakistan)

Engineering Computations

ISSN: 0264-4401

Article publication date: 29 September 2022

Issue publication date: 15 November 2022

122

Abstract

Purpose

In this article, the authors aims to introduce a novel Vieta–Lucas wavelets method by generalizing the Vieta–Lucas polynomials for the numerical solutions of fractional linear and non-linear delay differential equations on semi-infinite interval.

Design/methodology/approach

The authors have worked on the development of the operational matrices for the Vieta–Lucas wavelets and their Riemann–Liouville fractional integral, and these matrices are successfully utilized for the solution of fractional linear and non-linear delay differential equations on semi-infinite interval. The method which authors have introduced in the current paper utilizes the operational matrices of Vieta–Lucas wavelets to converts the fractional delay differential equations (FDDEs) into a system of algebraic equations. For non-linear FDDE, the authors utilize the quasilinearization technique in conjunction with the Vieta–Lucas wavelets method.

Findings

The purpose of utilizing the new operational matrices is to make the method more efficient, because the operational matrices contains many zero entries. Authors have worked out on both error and convergence analysis of the present method. Procedure of implementation for FDDE is also provided. Furthermore, numerical simulations are provided to illustrate the reliability and accuracy of the method.

Originality/value

Many engineers or scientist can utilize the present method for solving their ordinary or Caputo–fractional differential models. To the best of authors’ knowledge, the present work has not been used or introduced for the considered type of differential equations.

Keywords

Citation

Idrees, S. and Saeed, U. (2022), "Vieta–Lucas wavelets method for fractional linear and nonlinear delay differential equations", Engineering Computations, Vol. 39 No. 9, pp. 3211-3231. https://doi.org/10.1108/EC-02-2022-0094

Publisher

:

Emerald Publishing Limited

Copyright © 2022, Emerald Publishing Limited

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