Cover Image

Optimal routh-hurwitz conditions and picard’s successive approximation method for system of fractional differential equations

Fractional calculusisabranchofmathematicalanalysisinvestigatingthederivatives and integralsofarbitraryorder.Fractionalcalculushasawideapplicationsincemany realistic phenomenaaredefinedinfractionalorderderivativeandintegral.Moreover, fractional differentialequationsprovideanexcellentframeworkfordi...

Full description

Saved in:
Bibliographic Details
Main Author: Ng, Yong Xian
Format: Thesis
Language:English
English
English
Published: 2022
Subjects:
QA273-280 Probabilities. Mathematical statistics
Online Access:http://eprints.uthm.edu.my/8455/1/24p%20NG%20YONG%20XIAN.pdf
http://eprints.uthm.edu.my/8455/2/NG%20YONG%20XIAN%20COPYRIGHT%20DECLARATION.pdf
http://eprints.uthm.edu.my/8455/3/NG%20YONG%20XIAN%20WATERMARK.pdf
http://eprints.uthm.edu.my/8455/
Tags: Add Tag
No Tags, Be the first to tag this record!
id my.uthm.eprints.8455
record_format eprints
spelling my.uthm.eprints.84552023-02-27T02:33:56Z http://eprints.uthm.edu.my/8455/ Optimal routh-hurwitz conditions and picard’s successive approximation method for system of fractional differential equations Ng, Yong Xian QA273-280 Probabilities. Mathematical statistics Fractional calculusisabranchofmathematicalanalysisinvestigatingthederivatives and integralsofarbitraryorder.Fractionalcalculushasawideapplicationsincemany realistic phenomenaaredefinedinfractionalorderderivativeandintegral.Moreover, fractional differentialequationsprovideanexcellentframeworkfordiscussingthe possibility ofunlimitedmemoryandhereditaryproperties,consideringmoredegrees of freedom.Inthisthesis,thestabilitycriteriaofthefractionalShimizu-Morioka system andfractionaloceancirculationmodelinthesenseofCaputoderivative are developedanalyticallyusingoptimalRouth-Hurwitzconditions.Hence,Routh- Hurwitz conditionsforcubicandquadraticpolynomialsarepresented.Theadvantage of Routh-Hurwitzconditionsisthattheyallowonetoobtainstabilityconditions without solvingthefractionaldifferentialequations.Inthiscase,wefindthecritical range foradjustablecontrolparameterandfractionalorder �, whichconcludesthat the equilibriaofsystemsarelocallyasymptoticallystable.Aftermath,thenumerical results arepresentedtosupportourtheoreticalconclusionsusingtheAdams-type predictor-correctormethod.Ontheotherhand,wederivetheanalyticalsolutionfor the inhomogeneoussystemofdifferentialequationswithincommensuratefractional order 1 < �;�< 2, wherethefractionalorders � and � are uniqueandindependent of eachother.ThesystemsarefirstwritteninVolterraintegralequationsofthesecond kind. Further,Picard’ssuccessiveapproximationmethodisperformed,whichisan explicitanalyticalmethodthatconvergesveryclosetoexactsolutions,andthesolution is derivedinmultipleseriesandsomespecialfunctionexpressions,suchasGamma function, Mittag-Lefflerfunctionsandhypergeometricfunctions.Somespecialcases are discussedwhereallthesolutionsareverifiedusingsubstitution. 2022-07 Thesis NonPeerReviewed text en http://eprints.uthm.edu.my/8455/1/24p%20NG%20YONG%20XIAN.pdf text en http://eprints.uthm.edu.my/8455/2/NG%20YONG%20XIAN%20COPYRIGHT%20DECLARATION.pdf text en http://eprints.uthm.edu.my/8455/3/NG%20YONG%20XIAN%20WATERMARK.pdf Ng, Yong Xian (2022) Optimal routh-hurwitz conditions and picard’s successive approximation method for system of fractional differential equations. Doctoral thesis, Universiti Tun Hussein Onn Malaysia.
institution Universiti Tun Hussein Onn Malaysia
building UTHM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Tun Hussein Onn Malaysia
content_source UTHM Institutional Repository
url_provider http://eprints.uthm.edu.my/
language English
English
English
topic QA273-280 Probabilities. Mathematical statistics
spellingShingle QA273-280 Probabilities. Mathematical statistics
Ng, Yong Xian
Optimal routh-hurwitz conditions and picard’s successive approximation method for system of fractional differential equations
description Fractional calculusisabranchofmathematicalanalysisinvestigatingthederivatives and integralsofarbitraryorder.Fractionalcalculushasawideapplicationsincemany realistic phenomenaaredefinedinfractionalorderderivativeandintegral.Moreover, fractional differentialequationsprovideanexcellentframeworkfordiscussingthe possibility ofunlimitedmemoryandhereditaryproperties,consideringmoredegrees of freedom.Inthisthesis,thestabilitycriteriaofthefractionalShimizu-Morioka system andfractionaloceancirculationmodelinthesenseofCaputoderivative are developedanalyticallyusingoptimalRouth-Hurwitzconditions.Hence,Routh- Hurwitz conditionsforcubicandquadraticpolynomialsarepresented.Theadvantage of Routh-Hurwitzconditionsisthattheyallowonetoobtainstabilityconditions without solvingthefractionaldifferentialequations.Inthiscase,wefindthecritical range foradjustablecontrolparameterandfractionalorder �, whichconcludesthat the equilibriaofsystemsarelocallyasymptoticallystable.Aftermath,thenumerical results arepresentedtosupportourtheoreticalconclusionsusingtheAdams-type predictor-correctormethod.Ontheotherhand,wederivetheanalyticalsolutionfor the inhomogeneoussystemofdifferentialequationswithincommensuratefractional order 1 < �;�< 2, wherethefractionalorders � and � are uniqueandindependent of eachother.ThesystemsarefirstwritteninVolterraintegralequationsofthesecond kind. Further,Picard’ssuccessiveapproximationmethodisperformed,whichisan explicitanalyticalmethodthatconvergesveryclosetoexactsolutions,andthesolution is derivedinmultipleseriesandsomespecialfunctionexpressions,suchasGamma function, Mittag-Lefflerfunctionsandhypergeometricfunctions.Somespecialcases are discussedwhereallthesolutionsareverifiedusingsubstitution.
format Thesis
author Ng, Yong Xian
author_facet Ng, Yong Xian
author_sort Ng, Yong Xian
title Optimal routh-hurwitz conditions and picard’s successive approximation method for system of fractional differential equations
title_short Optimal routh-hurwitz conditions and picard’s successive approximation method for system of fractional differential equations
title_full Optimal routh-hurwitz conditions and picard’s successive approximation method for system of fractional differential equations
title_fullStr Optimal routh-hurwitz conditions and picard’s successive approximation method for system of fractional differential equations
title_full_unstemmed Optimal routh-hurwitz conditions and picard’s successive approximation method for system of fractional differential equations
title_sort optimal routh-hurwitz conditions and picard’s successive approximation method for system of fractional differential equations
publishDate 2022
url http://eprints.uthm.edu.my/8455/1/24p%20NG%20YONG%20XIAN.pdf
http://eprints.uthm.edu.my/8455/2/NG%20YONG%20XIAN%20COPYRIGHT%20DECLARATION.pdf
http://eprints.uthm.edu.my/8455/3/NG%20YONG%20XIAN%20WATERMARK.pdf
http://eprints.uthm.edu.my/8455/
_version_ 1758952410629275648
score 13.18916

Similar Items