Handbook of Fractional Calculus with Applications: Applications in Engineering, Life and Social Sciences, Part B (De Gruyter Reference)

295 Pages·2019·14.376 MB·English

by  Dumitru Bǎleanu (editor), António Mendes Lopes (editor)

DumitruBaleanu,AntónioMendesLopes(Eds.)
HandbookofFractionalCalculuswithApplications
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Handbookof Fractional Calculus with Applications
EditedbyJ.A.TenreiroMachado
Volume1:Theory
AnatolyKochubei,YuriLuchko(Eds.),2019
ISBN978-3-11-057081-6,e-ISBN(PDF)978-3-11-057162-2,
e-ISBN(EPUB)978-3-11-057063-2
Volume2:FractionalDifferentialEquations
AnatolyKochubei,YuriLuchko(Eds.),2019
ISBN978-3-11-057082-3,e-ISBN(PDF)978-3-11-057166-0,
e-ISBN(EPUB)978-3-11-057105-9
Volume3:NumericalMethods
GeorgeEmKarniadakis(Ed.),2019
ISBN978-3-11-057083-0,e-ISBN(PDF)978-3-11-057168-4,
e-ISBN(EPUB)978-3-11-057106-6
Volume4:ApplicationsinPhysics,PartA
VasilyE.Tarasov(Ed.),2019
ISBN978-3-11-057088-5,e-ISBN(PDF)978-3-11-057170-7,
e-ISBN(EPUB)978-3-11-057100-4
Volume5:ApplicationsinPhysics,PartB
VasilyE.Tarasov(Ed.),2019
ISBN978-3-11-057089-2,e-ISBN(PDF)978-3-11-057172-1,
e-ISBN(EPUB)978-3-11-057099-1
Volume6:ApplicationsinControl
IvoPetráš(Ed.),2019
ISBN978-3-11-057090-8,e-ISBN(PDF)978-3-11-057174-5,
e-ISBN(EPUB)978-3-11-057093-9
Volume7:ApplicationsinEngineering,LifeandSocialSciences,PartA
DumitruBaleanu,AntónioMendesLopes(Eds.),2019
ISBN978-3-11-057091-5,e-ISBN(PDF)978-3-11-057190-5,
e-ISBN(EPUB)978-3-11-057096-0
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Dumitru Baleanu, António Mendes Lopes (Eds.)
Handbook of
Fractional Calculus
with Applications
|
Volume 8: Applications in Engineering, Life and Social
Sciences, Part B
Series edited by Jose Antonio Tenreiro Machado
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Editors
Prof.Dr.DumitruBaleanu Prof.Dr.AntónioMendesLopes
ÇankayaUniversity UniversityofPorto
FacultyofArtsandSciences FacultyofEngineering
DepartmentofMathematics Dept.ofMechanicalEngineering
ÖğretmenlerCaddesi14 RuaDr.RobertoFrias
06530Ankara 4003-465Porto
Turkey Portugal
[email protected] [email protected]
SeriesEditor
Prof.Dr.JoseAntonioTenreiroMachado
DepartmentofElectricalEngineering
InstitutoSuperiordeEngenhariadoPorto
InstitutoPolitécnicodoPorto
4200-072Porto
Portugal
[email protected]
ISBN978-3-11-057092-2
e-ISBN(PDF)978-3-11-057192-9
e-ISBN(EPUB)978-3-11-057107-3
LibraryofCongressControlNumber:2019934659
BibliographicinformationpublishedbytheDeutscheNationalbibliothek
TheDeutscheNationalbibliothekliststhispublicationintheDeutscheNationalbibliografie;
detailedbibliographicdataareavailableontheInternetathttp://dnb.dnb.de.
©2019WalterdeGruyterGmbH,Berlin/Boston
Coverimage:djmilic/iStock/GettyImagesPlus
Typesetting:VTeXUAB,Lithuania
Printingandbinding:CPIbooksGmbH,Leck
www.degruyter.com
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Preface
FractionalCalculus(FC)hasoriginatedin1695,nearlyatthesametimeasconven-
tionalcalculus.However,FCattractedlimitedattentionandremainedapuremath-
ematicalexerciseinspiteoftheoriginalcontributionsofimportantmathematicians,
physicistsandengineers.FChadarapiddevelopmentduringthelastfewdecades,
bothinmathematicsandappliedsciences,beingnowadaysrecognizedasanexcel-
lenttoolfordescribingcomplexsystems,phenomenainvolvinglongrangememory
effectsandnon-locality.Ahugenumberofresearchpapersandbooksdevotedtothis
subjecthavebeenpublished,andpresentlyseveralspecializedconferencesandwork-
shopsarebeingorganizedeachyear.TheFCpopularityinallfieldsofscienceisdue
toitssuccessfulapplicationinmathematicalmodels,namelyintheformofFCoper-
atorsandfractionalintegralanddifferentialequations.Presently,wearewitnessing
considerableprogressbothontheoreticalaspectsandapplicationsofFCinareassuch
asphysics,engineering,biology,medicine,economy,andfinance.
ThepopularityofFChasattractedmanyresearchersfromallovertheworldand
thereisademandforworkscoveringallareasofscienceinasystematicandrigorous
form. In fact, the literature devoted to FC and its applications is huge, but readers
areconfrontedwithahighheterogeneity.TheHandbookofFractionalCalculuswith
Applications(HFCA)intendstofillthatgapandprovidesthereaderwithasolidand
systematictreatmentofthemainaspectsandapplicationsofFC.Motivatedbythese
ideas,theeditorsofthevolumesinvolvedateamofinternationallyrecognizedexperts
forajointpublishingprojectofferingasurveyoftheirownandotherimportantresults
intheirfieldsofresearch.Asaresultofthesejointefforts,amodernencyclopediaof
FCanditsapplications,reflectingthecoreofthepresentdayscientificknowledge,is
nowavailablewiththeHFCA.Thisworkisdistributedineightdistinctvolumes,each
onedevelopedunderthesupervisionofitseditors.
TheeighthvolumeofHFCAincludes11chaptersonFCapplicationsinengineer-
ing, life and social sciences. The volume starts with an interesting chapter on eco-
nomicmodelswithpower-lawmemory.Thenextthreechaptersaretoplevelcontri-
butionsaddressingfractorsandtheirapplicationsinfractional-ordercircuits,energy
harvestingindynamicalsystems,andfractionalmodelsofchargekineticsinsuper-
capacitors.Thefollowingisagroupoffourchaptersonsignalprocessing.Thereader
willfindstateofthearttechniquesforfractionalsignalsandsystems,signalprediction
usingfractionalmodels,andspectralmethodswithinFC.Thenexttwochaptersad-
dressthedesignandgenerationofthefractional-ordermulti-scrollchaoticattractors,
and discrete fractional masks with applications to image enhancement. One chap-
terdiscussingtheexistencetheoryforfractionaldifferentialequationswithnon-local
integro-multipointboundaryconditionswithapplicationsendsthevolume.
Ourspecialthanksgototheauthorsofindividualchapters,whichareexcellent
surveys of selected classical and new results in several important fields of FC. The
https://doi.org/10.1515/9783110571929-201
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VI | Preface
editorsbelievethattheHFCAwillrepresentavaluableandreliablereferenceworkfor
allscholarsandprofessionalswillingtoengageinresearchinthischallengingand
timelyscientificarea.
DumitruBaleanuandAntónioMendesLopes
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Contents
Preface|V
VasilyE.Tarasov
Economicmodelswithpower-lawmemory|1
AvishekAdhikaryandKarabiBiswas
Four-quadrantfractorsandtheirapplicationsinfractionalordercircuits|33
GrzegorzLitak,CedrickA.K.Kwuimy,andBenjaminDucharne
Energyharvestingindynamicalsystemswithfractional-orderphysical
properties|63
RenatT.SibatovandVladimirV.Uchaikin
Fractionalkineticsofchargecarriersinsupercapacitors|87
GabrielBengochea,ManuelOrtigueira,LuisVerde-Star,andAntónioM.Lopes
Recursive-operationalmethodforfractionalsystems|119
ManuelD.Ortigueira,J.TenreiroMachado,FernandoJ.V.Coito,andGabriel
Bengochea
Discrete-timefractionalsignalsandsystems|149
TomasSkovranekandVladimirDespotovic
Signalpredictionusingfractionalderivativemodels|179
E.H.Doha,M.A.Zaky,andM.A.Abdelkawy
Spectralmethodswithinfractionalcalculus|207
LipingChenandRanchaoWu
Designandgenerationoffractional-ordermulti-scrollchaoticattractors|233
Guo-ChengWu,DumitruBaleanu,andYun-RuBai
Discretefractionalmasksandtheirapplicationstoimageenhancement|261
BashirAhmad,SotirisK.Ntouyas,andAhmedAlsaedi
Existencetheoryforfractionaldifferentialequationswithnonlocal
integro-multipointboundaryconditionswithapplications|271
Index|283
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