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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محفوظ في:
التفاصيل البيبلوغرافية
المؤلف الرئيسي: Ng, Yong Xian
التنسيق: أطروحة
اللغة:English
English
English
منشور في: 2022
الموضوعات:
الوصول للمادة أونلاين: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
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الوصف
الملخص: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.