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1、LectureNotesinMathematics2004Editors:J.-M.Morel,CachanF.Takens,GroningenB.Teissier,ParisKaiDiethelmTheAnalysisofFractionalDifferentialEquationsAnApplication-OrientedExpositionUsingDifferentialOperatorsofCaputoType123KaiDiethelmGNSGesellschaftfurNumerischeSimula
2、tionmbH¨AmGau?berg238114BraunschweigGermanydiethelm@gns-mbh.comISBN:978-3-642-14573-5e-ISBN:978-3-642-14574-2DOI:10.1007/978-3-642-14574-2SpringerHeidelbergDordrechtLondonNewYorkLectureNotesinMathematicsISSNprintedition:0075-8434ISSNelectronicedition:1617-9692L
3、ibraryofCongressControlNumber:2010933969MathematicsSubjectClassi?cation(2010):34A08,34A12,34-02,34-01,26A33,33E12cSpringer-VerlagBerlinHeidelberg2010Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,speci?callyther
4、ightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicro?lmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurre
5、ntversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliabletoprosecutionundertheGermanCopyrightLaw.Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspeci?cstatement,thatsuchnam
6、esareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Coverdesign:SPiPublisherServicesPrintedonacid-freepaperspringer.comPrefaceThereisauniverseofmathematicslyinginbetweenthecompletedifferentiationsandintegrations.O.HeavisideThisbo
7、okisdevotedtosomequestionsinFractionalCalculus,thatis,thetheoryofdifferentialandintegraloperatorsofnon-integerorder,andinparticulartodiffer-entialequationscontainingsuchoperators.Eventhoughthe?rststepsofthetheoryitselfdatebacktothe?rsthalfofthenineteenthcentury
8、,thesubjectonlyreallycametolifeoverthelastfewdecades.Aparticularfeatureisthatengineersandscien-tistshavedevelopednewmodelsthatinvolvefractionaldifferentialequations.Thesemod
