資產(chǎn)證券化（abs）與資產(chǎn)支持票據(jù)（abn）實(shí)務(wù)操作及案例分析

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1、ExistenceofSolutionsofFractionalFunctionalDi?erentialEquationswithCausalOperatorsCandidateSupervisorCollegeProgramLuoXianNanProfessorZhouYongMathematicsandComputationalScienceAppliedMathematicsSpecialityTheoryandApplicationofFunctionalDi?erentialEquationsDegreeUniversityDatePh.D.

2、degreeofScienceXiangTanUniversityApril,2011BanachKrasnoselskiiIRiemann-LiouvilleCaputoAbstractDuringthepastdecades,withthedevelopmentoffractionalcalculus,frac-tionaldi?erentialequationshaveddevelopedrapidlyduetoitsapplicationinvarioussciences.Althoughalotofresultshavebeenobtained

3、fortheexistenceofsolutionsforfunctionaldi?erentialequationswithcausaloperators,theresultsfortheinitialvalueproblemsoffractionalfunctionaldi?erentialequationswithcausaloperatorsisscarce.Thisdissertationfocusesontheexistenceofsolutionsoffractionalfunctionaldi?erentialequationswithcau

4、saloperators.Thisthesisconsistsoffourchapters.Maincontentsareorganizedasfollows:Inchapter1,we?rstintroducethebasicconceptsforthefractionalcalculusandfractionaldi?erentialequations,thede?nitionandpropertiesofthecausaloperator.Next,wealsointroducesomeapplicationbackgroundforfractiona

5、ldi?erentialequationsandsomeimportant?xedtheorems.Finally,weintroducethemainworkofthisthesis.Inchapter2,wediscussinitialvalueproblemforfractionalfunctionaldi?er-entialequationswhichcontainscausaloperatorinBanachspace.We?rstestab-lishafractionalintegralequationswhichisequivalenttoth

6、efractionalfunctionaldi?erentialequations.Byusingthetheoryoffractionalcalculusandmeasureofnoncompactness,weobtaintheexistenceresultsofsolutionsforfractionaldif-ferentialsystems.Wealsodiscussthecontinuationofsolutionsforfractionalfunctionaldi?erentialsystems.Inchapter3,westudyinitia

7、lvalueproblemforneutralfractionalfunctionaldi?erentialequationwithcausaloperator.Basedonthetheoryoffractionalcalculus,weestablishafractionalintegralequationwhichisequivalenttothefractionalfunctionaldi?erentialequations.ByusingKrasnoselskii’s?xedpointtheorem,weobtaintheexistenceandu

8、niquenessresultsofsolution