一类分数阶脉冲微分包含解的存在性-论文.pdf

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1、应用数学MATHEMATICAAPPLICATA2013。26(4)：828-838TheExistenceofSolutionsforImpulsiveFractionalDifferentialInclusionsZHUYan(~彦)，WANGLianglong(王良龙)(SchoolofMathematicalSciences，AnhuiUniversity，Hefei230601，China)Abstract：Thispaperisconcernedwiththeexistenceofsolutionsforimpulsivefractiona

2、ldifferenti．alinclusions(IFDIsforshort)．Abetterpresentationformulaofsolutionsforimpu1sivefractionaldifferentialequationsisgiven．BythemeansofnonlinearalternativeLeray-SchaudertypeandPC-typeAscoli—ArzelaTheorem，theexistenceofsolutionsforIFDIsisestablishedwhenthemulti-val—uedrighth

3、andsidehasconvexvalues．Thecompactnessofthesolutionsetisalsoobtained．Twoex—amplesaregiventoillustratethemainresults．Keywords：Fractionaldifferentialinclusion；Impulsiveproblem；Initialva1ueprob—lem；Existence；FixedpointCLCNumber：O175．14AMS(2000)SubjectClassification：26A33；34B37Docume

4、ntcode：AArticleID：1001—9847(2013)04—0828—111．IntroductionInthepaper，wewillstudytheexistenceofsolutionsforthefollowinginitia1va1ueDrob—lem(IVPforshort)forIFDIs．Precisely，weconsiderthefollowingproblem，fD，rY(￡)：===。D()∈F(t，)，a．e．∈J一八(l，⋯，)，J：一Co，6]，0

5、(0)一n，whereDistheCaputofractionalderivative，F：J×RR)isamuhi-valuedmaDwithconvexvalues(R)isthefamilyofallnonemptysubsetsofR)，Ik∈C(R，R)，k一1，⋯，，andn∈R，0一to

6、aldifferentialequationshaverecentlyprovedtobevaluabletools，duetoitsex—tensiveapplicationsinengineeringandscience．Formoredetails0nfractiona1calculustheorv，Receiveddate：Jan14，2013Foundationitem：SupportedbytheNaturalScienceFoundationofChina(10771001)，theAnhuiProvin—cialNaturalScien

7、ceFoundation(1308085MA01)，andtheResearchFundforDoctorStationofMinistryofEducationofChina(20113401110001)Biography：ZHUYan，female，Han，Jiangsu，majorindifferentialequationsanddynamicalsystems．No．4ZHUYaneta1．：TheExistenceofSolutionsforFractionalDiferentialInclusions829onecanseethemon

8、ographsofKilbaseta1．[¨，Diethelmc。]andTarasov[．I