A New Fractional Integration Operational Matrix of Chebyshev Wavelets in Fractional Delay Systems

A New Fractional Integration Operational Matrix of Chebyshev Wavelets in Fractional Delay Systems

Fractional integration operational matrix of Chebyshev wavelets based on the Riemann−Liouville fractional integral operator is derived directly from Chebyshev wavelets for the first time. The formulation is accurate and can be applied for fractional orders or an integer order. Using the fr...

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Main Author: Iman Malmir
Format: Article
Language:English
Published: MDPI AG 2019-09-01
Series:Fractal and Fractional
Subjects:
fractional integration operational matrix of Chebyshev wavelets
Chebyshev wavelets method
fractional time-delay optimal control
multifractional delay differential equation
quadratically constrained linear-quadratic optimal control
piecewise delay
Online Access:https://www.mdpi.com/2504-3110/3/3/46
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spelling doaj-d92994d66e7e4befb44d219808b570a92021-04-02T05:56:29ZengMDPI AGFractal and Fractional2504-31102019-09-01334610.3390/fractalfract3030046fractalfract3030046A New Fractional Integration Operational Matrix of Chebyshev Wavelets in Fractional Delay SystemsIman Malmir0Department of Mechanical Engineering, Buali Sina University, Hamedan, IranFractional integration operational matrix of Chebyshev wavelets based on the Riemann−Liouville fractional integral operator is derived directly from Chebyshev wavelets for the first time. The formulation is accurate and can be applied for fractional orders or an integer order. Using the fractional integration operational matrix, new Chebyshev wavelet methods for finding solutions of linear-quadratic optimal control problems and analysis of linear fractional time-delay systems are presented. Different numerical examples are solved to show the accuracy and applicability of the new Chebyshev wavelet methods.https://www.mdpi.com/2504-3110/3/3/46fractional integration operational matrix of Chebyshev waveletsChebyshev wavelets methodfractional time-delay optimal controlmultifractional delay differential equationquadratically constrained linear-quadratic optimal controlpiecewise delay
collection DOAJ
language English
format Article
sources DOAJ
author Iman Malmir
spellingShingle Iman Malmir
A New Fractional Integration Operational Matrix of Chebyshev Wavelets in Fractional Delay Systems
Fractal and Fractional
fractional integration operational matrix of Chebyshev wavelets
Chebyshev wavelets method
fractional time-delay optimal control
multifractional delay differential equation
quadratically constrained linear-quadratic optimal control
piecewise delay
author_facet Iman Malmir
author_sort Iman Malmir
title A New Fractional Integration Operational Matrix of Chebyshev Wavelets in Fractional Delay Systems
title_short A New Fractional Integration Operational Matrix of Chebyshev Wavelets in Fractional Delay Systems
title_full A New Fractional Integration Operational Matrix of Chebyshev Wavelets in Fractional Delay Systems
title_fullStr A New Fractional Integration Operational Matrix of Chebyshev Wavelets in Fractional Delay Systems
title_full_unstemmed A New Fractional Integration Operational Matrix of Chebyshev Wavelets in Fractional Delay Systems
title_sort new fractional integration operational matrix of chebyshev wavelets in fractional delay systems
publisher MDPI AG
series Fractal and Fractional
issn 2504-3110
publishDate 2019-09-01
description Fractional integration operational matrix of Chebyshev wavelets based on the Riemann−Liouville fractional integral operator is derived directly from Chebyshev wavelets for the first time. The formulation is accurate and can be applied for fractional orders or an integer order. Using the fractional integration operational matrix, new Chebyshev wavelet methods for finding solutions of linear-quadratic optimal control problems and analysis of linear fractional time-delay systems are presented. Different numerical examples are solved to show the accuracy and applicability of the new Chebyshev wavelet methods.
topic fractional integration operational matrix of Chebyshev wavelets
Chebyshev wavelets method
fractional time-delay optimal control
multifractional delay differential equation
quadratically constrained linear-quadratic optimal control
piecewise delay
url https://www.mdpi.com/2504-3110/3/3/46
work_keys_str_mv AT imanmalmir anewfractionalintegrationoperationalmatrixofchebyshevwaveletsinfractionaldelaysystems
AT imanmalmir newfractionalintegrationoperationalmatrixofchebyshevwaveletsinfractionaldelaysystems
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