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.
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Abstract
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.
Item Type: | Thesis (Doctoral) |
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Subjects: | Q Science > QA Mathematics > QA273-280 Probabilities. Mathematical statistics |
Divisions: | Faculty of Applied Science and Technology > Department of Physics and Chemistry |
Depositing User: | Mrs. Sabarina Che Mat |
Date Deposited: | 27 Feb 2023 02:33 |
Last Modified: | 27 Feb 2023 02:33 |
URI: | http://eprints.uthm.edu.my/id/eprint/8455 |
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