资产证券化（abs）与资产支持票据（abn）实务操作及案例分析

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1、ExistenceofSolutionsofFractionalFunctionalDifferentialEquationswithCausalOperatorsCandidateSupervisorCollegeProgramLuoXianNanProfessorZhouYongMathematicsandComputationalScienceAppliedMathematicsSpecialityTheoryandApplicationofFunctionalDifferentialEquationsDegreeUniversityDatePh.D.

2、degreeofScienceXiangTanUniversityApril,2011BanachKrasnoselskiiIRiemann-LiouvilleCaputoAbstractDuringthepastdecades,withthedevelopmentoffractionalcalculus,frac-tionaldifferentialequationshaveddevelopedrapidlyduetoitsapplicationinvarioussciences.Althoughalotofresultshavebeenobtained

3、fortheexistenceofsolutionsforfunctionaldifferentialequationswithcausaloperators,theresultsfortheinitialvalueproblemsoffractionalfunctionaldifferentialequationswithcausaloperatorsisscarce.Thisdissertationfocusesontheexistenceofsolutionsoffractionalfunctionaldifferentialequationswithcau

4、saloperators.Thisthesisconsistsoffourchapters.Maincontentsareorganizedasfollows:Inchapter1,wefirstintroducethebasicconceptsforthefractionalcalculusandfractionaldifferentialequations,thedefinitionandpropertiesofthecausaloperator.Next,wealsointroducesomeapplicationbackgroundforfractiona

5、ldifferentialequationsandsomeimportantfixedtheorems.Finally,weintroducethemainworkofthisthesis.Inchapter2,wediscussinitialvalueproblemforfractionalfunctionaldiffer-entialequationswhichcontainscausaloperatorinBanachspace.Wefirstestab-lishafractionalintegralequationswhichisequivalenttoth

6、efractionalfunctionaldifferentialequations.Byusingthetheoryoffractionalcalculusandmeasureofnoncompactness,weobtaintheexistenceresultsofsolutionsforfractionaldif-ferentialsystems.Wealsodiscussthecontinuationofsolutionsforfractionalfunctionaldifferentialsystems.Inchapter3,westudyinitia

7、lvalueproblemforneutralfractionalfunctionaldifferentialequationwithcausaloperator.Basedonthetheoryoffractionalcalculus,weestablishafractionalintegralequationwhichisequivalenttothefractionalfunctionaldifferentialequations.ByusingKrasnoselskii’sfixedpointtheorem,weobtaintheexistenceandu

8、niquenessresultsofsolution