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1、LectureNotesinElectricalEngineeringVolume84Forfurthervolumes:http://www.springer.com/series/7818ManuelDuarteOrtigueiraFractionalCalculusforScientistsandEngineers123ManuelDuarteOrtigueiraFaculdadedeCiências/TecnologiadaUNLUNINOVAandDEECampusdaFCTQuintadaTorre2829-516C
2、aparicaPortugale-mail:mdo@fct.unl.ptISSN1876-1100e-ISSN1876-1119ISBN978-94-007-0746-7e-ISBN978-94-007-0747-4DOI10.1007/978-94-007-0747-4SpringerDordrechtHeidelbergLondonNewYorkÓSpringerScience+BusinessMediaB.V.2011Nopartofthisworkmaybereproduced,storedinaretrievalsys
3、tem,ortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,microfilming,recordingorotherwise,withoutwrittenpermissionfromthePublisher,withtheexceptionofanymaterialsuppliedspecificallyforthepurposeofbeingenteredandexecutedonacomputersystem,forexclusiveuse
4、bythepurchaserofthework.Coverdesign:eStudioCalamar,Berlin/FigueresPrintedonacid-freepaperSpringerispartofSpringerScience+BusinessMedia(www.springer.com)TothememoryofmyparentsJoséOrtigueiraandRitaRosadaAscençãoDuartethatdidtheirbestforme.TomychildrenEduardoandJoana,an
5、dmywife,Laurinda,fortheirloveandpatience.PrefaceFractionalCalculushasbeenattractingtheattentionofscientistsandengineersfromlongtimeago,resultinginthedevelopmentofmanyapplications.Sincetheninetiesoflastcenturyfractionalcalculusisbeingrediscoveredandappliedinanincreasi
6、ngnumberoffields,namelyinseveralareasofPhysics,ControlEngi-neering,andSignalProcessing.However,mostofthetheoreticalsetupofFrac-tionalCalculuswasdonebymathematiciansthatdirectedtheirattentionpreferablytotheso-calledRiemann-Liouvilleand/orCaputoderivatives.Wemustremarkt
7、hatmostofthearticlesthatappearinthescientificliterature,intheframeworkofthefractionalcalculusandtheirapplications,theauthorsusethosederivativesbutattheendtheycontrasttheirmodelusinganumericalapproachbasedinafinitenumberoftermsfromtheseriesthatdefinetheGrünwald-Letnikovd
8、erivative.Thismaybeconfirmedinseveralbooksthatappearedrecentlyandisonejusti-ficationforthepresentone.ItintendstopresentaFractionalCal
