On random fuzzy functional differential equationsOriginal Research Article111111.pdf

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1、Availableonlineatwww.sciencedirect.comFuzzySetsandSystems223(2013)8999www.elsevier.com/locate/fssOnrandomfuzzyfunctionaldifferentialequationsJongYeoulParka,JaeUgJeongb,∗aDepartmentofMathematics,BusanNationalUniversity,Busan609-735,SouthKoreabDepartmentofMathe

2、matics,DongeuiUniversity,Busan614-714,SouthKoreaReceived20December2011;receivedinrevisedform29January2013;accepted30January2013Availableonline8February2013AbstractInthispaper,weprovetheexistenceanduniquenessresultforrandomfuzzyfunctionaldifferentialequations.

3、Fortheexistenceanduniqueness,weusethemethodofsuccessiveapproximations.Somekindofboundednessofthesolutionisestablished.©2013ElsevierB.V.Allrightsreserved.Keywords:Fuzzyfunctionaldifferentialequation;Existenceanduniquenesstheorem;Fuzzystochasticprocess;Fuzzyran

4、domvariables;Randomfuzzydifferentialequation;Stochasticfuzzydifferentialequation1.IntroductionThetheoryoffuzzydifferentialequationshasbeeninitiatedasanindependentsubjectinconjunctionwithfuzzyvaluedanalysis[1,13]andset-valueddifferentialequations[6].UsingtheHu

5、kuharaderivativeofmulti-valuedfunc-tions,PuriandRalescu[17]haveintroducedtheconceptofH-differentiabilityforfuzzyfunctions.ThisconcepthasbeenstudiedandappliedincontextoffuzzydifferentialequationsbySeikkala[19]andKaleva[5]intimedependentform.Parketal.[15]studie

6、dtheapproximatesolutionsofthefuzzyfunctionalintegralequations.Parketal.[16]consideredtheexistenceofalmostperiodicsolutionsandasymptoticallyalmostperiodicsolutionsforfuzzyfunc-tionaldifferentialequations.Lupulescu[7]establishedthelocalandglobalexistenceanduniq

7、uenessresultsforfuzzyfunctionaldifferentialequations.Feng[4]consideredfuzzystochasticdifferentialsystemsusinganotionofmean-squarederivativeandmean-squareintegralofsecond-orderfuzzystochasticprocessesintroducedbyhimselfin[3].InFei[2]theexistenceanduniquenessof

8、thesolutionforrandomfuzzydifferentialequationswithnon-Lipschitzcoefficientsisgiven.In[810]onecanfindresearchconcerningrandomfuzzydifferentialequationswhichcanbeappropriateinthemodelingofdyn