两类分数阶微分方程解的存在性

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1、华中科技大学硕士学位论文两类分数阶微分方程解的存在性姓名：王晓娜申请学位级别：硕士专业：应用数学指导教师：刘斌2011-04-23=,
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5,tkRiemann−LiouvilleVaVly">Mittag−Leffler4ViwIAbstractInrecentdecades,fractionaldifferentialequationshavebecomeanimportantsubjectduetotheirapplicationinvarioussciencesandhavebeenwidelyconcerned,theresearchoffractionaldifferentialequat

4、ionshasastrongpracticalsignificance.Thispapermainlystudiestheexistenceofsolutionsfortwokindsoffractionalorderdifferentialequations.Inthefirstsection,thepapergivesthehistoricalbackgroundandsignificance,andcurrentsituationoftheproblemwestudied.Inthesecondsection,therelevan

5、tdefinitionsandtheoremsusedinthisarticlearegiven,theyarepreparedtothefollowingmainconclusionstobeproved.Inthethirdsection,westudytheexistenceofsolutionsforfractionalorderfunctionaldifferentialequationswithfinitedelay,wetransformthefractionalorderfunctionaldifferentialequ

6、ationsintointegralequationsbytherelatedlemma,wedefinetheappropriateintegraloperatorinproductspace,thenbasedoncertainconditionstheexistenceanduniquenessofsolutionsareobtainedbymeansoftheBanachcontractionmappingprincipleLeary-SchauderfixedpointtheoremandSchauderfixedpoin

7、ttheorem,theresultsthatareobtainedonbasisoftheotherliteraturesaresomenewresults,relevantexamplesaregiventoillustratetheconclusions.Inthefourthsection,wealsodiscusstheexistenceofquasi-solutionsoffractionalorderdifferentialequation,wegivethedefinitionofquasi-solutionsoff

8、ractionalorderdifferentialequation,therelatedlemmaisobtainedbythedefinitionofMittag-Lefflerfunctioninfractionaldifferentialequations,ont