A new operational matrices-based spectral method for multi-order fractional problems

The operational matrices-based computational algorithms are the promising tools to tackle the problems of non-integer derivatives and gained a substantial devotion among the scientific community. Here, an accurate and efficient computational scheme based on another new type of polynomial with the he...

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Main Authors: Hamid, M., Foong, O.M., Usman, M., Khan, I., Wang, W.
Format: Article
Institution: Universiti Teknologi Petronas
Record Id / ISBN-0: utp-eprints.30016 /
Published: MDPI AG 2020
Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85090994836&doi=10.3390%2fsym12091471&partnerID=40&md5=6c3def828e286c6c3a33b9ede71152a2
http://eprints.utp.edu.my/30016/
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spelling utp-eprints.300162022-03-25T03:18:09Z A new operational matrices-based spectral method for multi-order fractional problems Hamid, M. Foong, O.M. Usman, M. Khan, I. Wang, W. The operational matrices-based computational algorithms are the promising tools to tackle the problems of non-integer derivatives and gained a substantial devotion among the scientific community. Here, an accurate and efficient computational scheme based on another new type of polynomial with the help of collocation method (CM) is presented for different nonlinear multi-order fractional differentials (NMOFDEs) and Bagley-Torvik (BT) equations. The methods are proposed utilizing some new operational matrices of derivatives using Chelyshkov polynomials (CPs) through Caputo's sense. Two different ways are adopted to construct the approximated (AOM) and exact (EOM) operational matrices of derivatives for integer and non-integer orders and used to propose an algorithm. The understudy problems have been transformed to an equivalent nonlinear algebraic equations system and solved by means of collocation method. The proposed computational method is authenticated through convergence and error-bound analysis. The exactness and effectiveness of said method are shown on some fractional order physical problems. The attained outcomes are endorsing that the recommended method is really accurate, reliable and efficient and could be used as suitable tool to attain the solutions for a variety of the non-integer order differential equations arising in applied sciences. © 2020 by the authors. MDPI AG 2020 Article NonPeerReviewed https://www.scopus.com/inward/record.uri?eid=2-s2.0-85090994836&doi=10.3390%2fsym12091471&partnerID=40&md5=6c3def828e286c6c3a33b9ede71152a2 Hamid, M. and Foong, O.M. and Usman, M. and Khan, I. and Wang, W. (2020) A new operational matrices-based spectral method for multi-order fractional problems. Symmetry, 12 (9). http://eprints.utp.edu.my/30016/
institution Universiti Teknologi Petronas
collection UTP Institutional Repository
description The operational matrices-based computational algorithms are the promising tools to tackle the problems of non-integer derivatives and gained a substantial devotion among the scientific community. Here, an accurate and efficient computational scheme based on another new type of polynomial with the help of collocation method (CM) is presented for different nonlinear multi-order fractional differentials (NMOFDEs) and Bagley-Torvik (BT) equations. The methods are proposed utilizing some new operational matrices of derivatives using Chelyshkov polynomials (CPs) through Caputo's sense. Two different ways are adopted to construct the approximated (AOM) and exact (EOM) operational matrices of derivatives for integer and non-integer orders and used to propose an algorithm. The understudy problems have been transformed to an equivalent nonlinear algebraic equations system and solved by means of collocation method. The proposed computational method is authenticated through convergence and error-bound analysis. The exactness and effectiveness of said method are shown on some fractional order physical problems. The attained outcomes are endorsing that the recommended method is really accurate, reliable and efficient and could be used as suitable tool to attain the solutions for a variety of the non-integer order differential equations arising in applied sciences. © 2020 by the authors.
format Article
author Hamid, M.
Foong, O.M.
Usman, M.
Khan, I.
Wang, W.
spellingShingle Hamid, M.
Foong, O.M.
Usman, M.
Khan, I.
Wang, W.
A new operational matrices-based spectral method for multi-order fractional problems
author_sort Hamid, M.
title A new operational matrices-based spectral method for multi-order fractional problems
title_short A new operational matrices-based spectral method for multi-order fractional problems
title_full A new operational matrices-based spectral method for multi-order fractional problems
title_fullStr A new operational matrices-based spectral method for multi-order fractional problems
title_full_unstemmed A new operational matrices-based spectral method for multi-order fractional problems
title_sort new operational matrices-based spectral method for multi-order fractional problems
publisher MDPI AG
publishDate 2020
url https://www.scopus.com/inward/record.uri?eid=2-s2.0-85090994836&doi=10.3390%2fsym12091471&partnerID=40&md5=6c3def828e286c6c3a33b9ede71152a2
http://eprints.utp.edu.my/30016/
_version_ 1741197336428675072
score 11.62408

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