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

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...

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Main Author: Ng, Yong Xian
Format: Thesis
Language:English
English
English
Published: 2022
Subjects:
QA273-280 Probabilities
Mathematical statistics
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spelling my-uthm-ep.84552023-02-27T02:33:56Z Optimal routh-hurwitz conditions and picard’s successive approximation method for system of fractional differential equations 2022-07 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 http://eprints.uthm.edu.my/8455/ http://eprints.uthm.edu.my/8455/1/24p%20NG%20YONG%20XIAN.pdf text en public http://eprints.uthm.edu.my/8455/2/NG%20YONG%20XIAN%20COPYRIGHT%20DECLARATION.pdf text en staffonly http://eprints.uthm.edu.my/8455/3/NG%20YONG%20XIAN%20WATERMARK.pdf text en validuser phd doctoral Universiti Tun Hussein Onn Malaysia Fakulti Sains Gunaan dan Teknologi
institution Universiti Tun Hussein Onn Malaysia
collection UTHM Institutional Repository
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
qualification_name Doctor of Philosophy (PhD.)
qualification_level Doctorate
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
granting_institution Universiti Tun Hussein Onn Malaysia
granting_department Fakulti Sains Gunaan dan Teknologi
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
_version_ 1776103349886648320

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