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1、AcceptedManuscriptRandomfuzzyfractionalintegralequationstheoreticalfoundationsMarekT.MalinowskiPII:S0165-0114(14)00426-6DOI:10.1016/j.fss.2014.09.019Reference:FSS6641Toappearin:FuzzySetsandSystemsReceiveddate:6December2013Reviseddate:9September2014Acceptedda
2、te:26September2014Pleasecitethisarticleinpressas:M.T.Malinowski,Randomfuzzyfractionalintegralequationstheoreticalfoundations,FuzzySetsandSystems(2014),http://dx.doi.org/10.1016/j.fss.2014.09.019ThisisaPDFfileofanuneditedmanuscriptthathasbeenacceptedforpublica
3、tion.Asaservicetoourcustomersweareprovidingthisearlyversionofthemanuscript.Themanuscriptwillundergocopyediting,typesetting,andreviewoftheresultingproofbeforeitispublishedinitsfinalform.Pleasenotethatduringtheproductionprocesserrorsmaybediscoveredwhichcouldaff
4、ectthecontent,andalllegaldisclaimersthatapplytothejournalpertain.Randomfuzzyfractionalintegralequations–theoreticalfoundationsMarekT.MalinowskiFacultyofMathematics,ComputerScienceandEconometrics,UniversityofZielonaG´ora,ul.Prof.Z.Szafrana4a,65-516ZielonaG´or
5、a,PolandE-mailaddresses:m.malinowski@wmie.uz.zgora.pl,malinowskimarek@poczta.fmAbstract:Thispaperpresentsmathematicalfoundationsforstudiesofrandomfuzzyfractionalintegralequationswhichinvolveafuzzyintegraloffractionalorder.Weconsidertwodifferentkindsofsuchequa
6、tions.Theirsolutionshavedifferentgeometricalproperties.Theequationsofthefirstkindpossesssolutionswithtrajectoriesofnondecreasingdiameteroftheirconsecutivevalues.Ontheotherhand,thesolutionstoequationsofthesecondkindhavetrajectorieswithnonincreasingdiameterofthe
7、irconsecutivevalues.Firstly,theexistenceanduniquenessofsolutionsisinvestigated.Thisisshowedbyusingamethodofsuccessiveapproximations.Anestimationoferrorofnthapproximationisgiven.Alsoaboundednessofthesolutionisindicated.Toshowwell-posednessoftheconsideredtheor
8、y,weprovethatsolutionsdependcontinuouslyonthedataoftheequations.Someconcreteexamplesofrandomfuzzyfractionalintegralequationsaresolvedexplicitly.Keywords:randomfuzzyfractionalintegralequation,exi
