具有非分离边界条件的非线性分数阶微分包含弱解的存在性

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1、CHINESEJoURNALOct．2014Vo1．31N0．5oFENGINEERINGMA，I’HEMATICSdof10．3969／j．issn．1005—3085．2014．05．015ArticleID：1005·-3085(2014)05-0779--12FractionalDirentialInclusionwithNon-separatedBoundaryConditions术ZHOUWen-xue1,2．LIUHai—zhong(1一CollegeofMathematicsandPhysics，LanzhouJia

2、otongUniversity，Lanzhou730070；2-SchoolofMathematicalSciences，Fuda_nUniversity,Shanghai200433)Abstract：Manypracticalproblems，suchaSthosefromphysics，aerospacescience，ecologicalscienceandengineering，needtobedescribedbyfractionaldiferentialequations，SOitisimportanttostudyt

3、heseequationsintheoryandimplement．Inthispaper，underthePettisintegrabilityaSsumption，wediscusstheexistenceofweaksolutiontotheboundaryvalueproblemforaclassofnonlinearfractionaldiferentialinclu—sioninvolvingnon—separatedboundaryconditions．ThediferentialoperatoristheCaputo

4、derivative，andthenonlineartermhaSweaklysequentiallyclosedgraph．TheanalysisreliesonMonch’Sfixedpointtheoremcombinedwiththetechniqueofmeasuresofweaknoncompactness．Finally，anexampleisgiventoillustratetheefectivenessoftheproposedmethod．Keywords：boundaryvalueproblem；fractio

5、naldiferentialinclusion；Caputofractionalderiva-tive；weaksolutionsClassification：AMS(2000)26A33；34B15CLCnumber：O175．8DOCl1InentCOde：A1IntroductionThispaperismainlyconcernedwiththeexistenceresultsforthe％llowingfractionaldiferentialinclusionwithnon—separatedboundarycondit

6、ions{CD。"u：(t)eF(t’：’二三+。≠，入。≠，(1)where1

7、archfield：theoryandapplicationofnonlinearfunctionalanalysis．F0andationitem：TheNationalNaturalScienceFoundationofChina(11161027；11262009；112261321：theNaturalScienceFoundationofGansuProvince(1308RJZA113)：theScientificResearchProjectsinCO-liegesandUniversitiesofGansuProvi

8、nce(2013A一043)；theFundamentalResearchFundsfortheCansuUniversities(212084；213061)；theYouthScienceFoundationofLanzhouJi