Fuzzy fractional functional differential equations under Caputo gH-differentiabilityOriginal Research Article111111.pdf

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1、CommunNonlinearSciNumerSimulat22(2015)1134–1157ContentslistsavailableatScienceDirectCommunNonlinearSciNumerSimulatjournalhomepage:www.elsevier.com/locate/cnsnsFuzzyfractionalfunctionaldifferentialequationsunderCaputogH-differentiabilityNgoVanHoaDivisionofComputationalMathematicsand

2、Engineering,InstituteforComputationalScience,TonDucThangUniversity,HoChiMinhCity,VietNamarticleinfoabstractArticlehistory:Inthispaperthefuzzyfractionalfunctionaldifferentialequations(FFFDEs)undertheReceived1December2013CaputogeneralizedHukuharadifferentiabilityareintroduced.Westudy

3、theexistenceReceivedinrevisedform5August2014anduniquenessresultsofsolutionsforFFFDEsundersomesuitableconditions.AlsotheAccepted8August2014solutiontofuzzyfractionalfunctionalinitialvalueproblemunderCaputo-typefuzzyAvailableonline4September2014fractionalderivativesbyamodifiedAdams–Bas

4、hforth–Moultonmethod(MABMM)ispresented.Themethodisillustratedbysolvingsomeexamples.Keywords:Ó2014ElsevierB.V.Allrightsreserved.FractionaldifferentialequationsFuzzyfunctionaldifferentialequationsLipschitzgeneralizedconditionAdams–Bashforth–Moultonmethod1.IntroductionThetheoryoffract

5、ionalcalculus,whichdealswiththeinvestigationandapplicationsofderivativesandintegralsofarbi-traryorderhasalonghistory.Thetheoryoffractionalcalculusdevelopedmainlyasapuretheoreticalfieldofmathematics,inthelastdecadesithasbeenusedinvariousfieldsasrheology,viscoelasticity,electrochemistr

6、y,diffusionprocesses,etc.Fractionalcalculusandfractionaldifferentialequationshaveundergoneexpandedstudyinrecentyearsasaconsiderableinterestbothinmathematicsandinapplications.Theywereappliedinmodelingofmanyphysicalandchemicalprocessesandinengineering.Oneoftherecentlyinfluentialworkso

7、nthesubjectoffractionalcalculusisthemonographofPodlubny[25]andtheotheristhemonographofKilbasetal.[32].Consequently,severalresearchpapersweredonetoinvestigatethetheoryandsolutionsoffractionaldifferentialequations(see[18,21,27]andreferencestherein).Inrealworldsystems,delayscanberecog

8、nizedeverywhereandtherehas