Table Of ContentFractional Dynamics and Control
Dumitru Baleanu • Jose´ Anto´nio Tenreiro Machado
Albert C. J. Luo
Editors
Fractional Dynamics
and Control
123
Editors
DumitruBaleanu Jose´Anto´nioTenreiroMachado
MathematicsandComputer DepartmentofElectrical
Sciences Engineering
FacultyofArtandSciences PolytechnicInstituteofPorto
CankayaUniversity InstituteofEngineering
Ankara RuaDrAnto´nioBernadino
Turkey Almeida431
[email protected] 4200-072Porto
Portugal
[email protected]
AlbertC.J.Luo
MechanicalandIndustrial
Engineering
SchoolofEngineering
SouthernIllinoisUniversity
Room:EB2064
Edwardsville
USA
[email protected]
ISBN978-1-4614-0456-9 e-ISBN978-1-4614-0457-6
DOI10.1007/978-1-4614-0457-6
SpringerNewYorkDordrechtHeidelbergLondon
LibraryofCongressControlNumber:2011941213
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Preface
Fractional calculus is as old as the classical one and it started to be intensively
studiedandappliedinmanybranchesofscienceandengineering.
Thefractionaldynamicsisgrowingfasterduringthefewdecadestogetherwith
the fractional control theory which certified the fractional calculus as being a
fundamentaltoolindescribingthedynamicsofcomplexsystems.
Thisbookisbasedonthe3rdconferenceonNonlinearScienceandComplexity
(NSC), Ankara, Turkey, July 27–31, 2010. Due to the impact of topics on a very
widespectrumofproblemsinscienceandengineering,thisconferenceprovideda
place to exchange recent developments, discoveries and progresses on nonlinear
science and complexity. This conference is the continuation of the first 2006
ConferenceonNonlinearScienceandComplexity,Beijing,China,andthesecond
2008conferenceonNonlinearScienceandComplexityheldinPorto,Portugal.
This book it is entitled “Fractional Dynamics and Control” and it collects the
recent development in nonlinear dynamics, nonlinear vibration and control. The
aimofthisbookprovidesafastexchangeideainnonlineardynamicalsystemsand
control.Onecanlearntherecentdevelopments,includinganalytical,numericaland
experimentalresultsinsucharea.
The editors hope that this collection of papers may be fruitful for scholars,
researchersandadvancedtechnicalmembersof industriallaboratoryfacilities, for
developingnewtoolsandproducts.
The editorsthankto the Rector and to the Presidentofthe Board of Trusteeof
CankayaUniversityaswellastotheScientificandTechnologicalResearchCouncil
ofTurkeyforthefinancialsupportneededtoholdthediscussionsanddebates.
DumitruBaleanu
Jose´ Anto´nioTenreiroMachado
AlbertC.J.Luo
v
Contents
PartI FractionalControl
1 AFormulationandNumericalScheme forFractional
OptimalControlofCylindricalStructuresSubjected
toGeneralInitialConditions ............................................. 3
Md.MehediHasan,X.W.Tangpong,andO.P.Agrawal
(cid:2) (cid:3)
2 NeuralNetwork-AssistedPI D Control ............................... 19
MehmetO¨nderEfe
3 Application of Backstepping Control Technique
toFractionalOrderDynamicSystems................................... 33
MehmetO¨nderEfe
4 ParameterTuning ofaFractional-OrderPIController
UsingtheITAECriteria ................................................... 49
BadreddineBoudjehemandDjalilBoudjehem
5 AFractionalModelPredictiveControlforFractional
OrderSystems .............................................................. 59
DjalilBoudjehemandBadreddineBoudjehem
6 ANoteontheSequentialLinearFractionalDynamical
SystemsfromtheControlSystemViewpointandL2 -Theory......... 73
AbolhassanRazminia,VahidJohariMajd,
andAhmadFeizDizaji
7 StabilizationofFractionalOrderUnifiedChaoticSystems
viaLinearStateFeedbackController.................................... 85
E.G.Razmjou,A.Ranjbar,Z.Rahmani,R.Ghaderi,
andS.Momani
vii
viii Contents
PartII FractionalVariationalPrinciples andFractional
DifferentialEquations
8 FractionalVariationalCalculusforNon-differentiableFunctions.... 97
AgnieszkaB.Malinowska
9 FractionalEuler–LagrangeDifferentialEquationsvia
CaputoDerivatives......................................................... 109
RicardoAlmeida,AgnieszkaB.Malinowska,andDelfim
F.M.Torres
10 StrictStabilityofFractionalPerturbedSystemsinTerms
ofTwoMeasures............................................................ 119
Cos¸kunYakar,MustafaBayramGu¨cen,andMuhammed
C¸ic¸ek
11 Initial Time Difference Strict Stability of Fractional
DynamicSystems........................................................... 133
Cos¸kunYakarandMustafaBayramGu¨cen
12 A FractionalOrder DynamicalTrajectoryApproach
forOptimizationProblemwithHPM .................................... 145
FıratEvirgenandNecatiO¨zdemir
PartIII FractionalCalculusinMathematicsandPhysics
13 OntheHadamardTypeFractionalDifferentialSystem............... 159
ZiqingGong,DeliangQian,ChangpinLi,andPengGuo
14 RobustSynchronizationandParameterIdentification
ofaUnifiedFractional-OrderChaoticSystem.......................... 173
E.G.Razmjou,A.Ranjbar,Z.Rahmani,andR.Ghaderi
15 FractionalCauchy Problemson Bounded Domains:
SurveyofRecentResults................................................... 185
ErkanNane
16 FractionalAnalogousModelsinMechanicsandGravityTheories... 199
DumitruBaleanuandSergiuI.Vacaru
17 Schro¨dingerEquationinFractionalSpace.............................. 209
SamiI.MuslihandOmP.Agrawal
18 SolutionsofWaveEquationinFractionalDimensionalSpace........ 217
SamiI.MuslihandOmP.Agrawal
19 FractionalExactSolutionsandSolitonsinGravity .................... 229
DumitruBaleanuandSergiuI.Vacaru
Contents ix
PartIV FractionalOrderModeling
20 FrontPropagationinanAutocatalytic
Reaction-SubdiffusionSystem ............................................ 239
IgorM.SokolovandDanielaFroemberg
21 NumericalSolutionofaTwo-DimensionalAnomalous
DiffusionProblem .......................................................... 249
NecatiO¨zdemirandDeryaAvcı
22 Analyzing Anomalous Diffusion in NMR
UsingaDistributionofRateConstants .................................. 263
R.L.Magin,Y.Z.Rawash,andM.N.Berberan-Santos
23 UsingFractionalDerivativestoGeneralize
theHodgkin–HuxleyModel ............................................... 275
HanyH.Sherief,A.M.A.El-Sayed,S.H.Behiry,
andW.E.Raslan
24 An Application of FractionalCalculus to Dielectric
RelaxationProcesses ....................................................... 283
M.S.C¸avus¸andS.Bozdemir
25 Fractional Wave Equation for Dielectric Medium
withHavriliak–NegamiResponse ........................................ 293
R.T.Sibatov,V.V.Uchaikin,andD.V.Uchaikin
Index............................................................................... 303
