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塔拉索夫 (Vasily E.Tarasov)、 罗朝俊 、伊布拉基莫夫 著 / 高等教育出版社 / 2010-08 / 精装
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分数维动力学(国内英文版)
NonlinearPhysicalSciencefocusesontherecentadvancesoffundamentaltheoriesandprinciples,analyticalandsymbolicapproaches,aswellascomputationaltechniquesinnonlinearphysicalscienceandnonlinearmathematicswithengineeringapplications.
PartIFractionfilContinuousModelsofFractalDistributions1FractionalIntegrationandFractals1.1Riemann-Liouvillefractionalintegrals1.2Liouvillefractionalintegrals1.3Rieszfractionalintegrals1.4Metricandmeasurespaces1.5Hausdorffmeasure1.6Hausdorffdimensionandfractals1.7Box-countingdimension1.8Massdimensionoffractalsystems1.9Elementarymodelsoffractaldistributions1.10Functionsandintegralsonfractals1.11Propertiesofintegralsonfractals1.12Integrationovernon-integer-dimensionalspace1.13Multi-variableintegrationonfractals1.14Massdistributiononfractals1.15DensityofstatesinEuclideanspace1.16Fractionalintegralandmeasureontherealaxis1.17Fractionalintegralandmassontherealaxis1.18Massoffractalmedia1.19Electricchargeoffractaldistribution1.20Probabilityonfractals1.21FractaldistributionofparticlesReferences2HydrodynamicsofFractalMedia2.1Introduction2.2Equationofbalanceofmass2.3Totaltimederivativeoffractionalintegral2.4Equationofcontinuityforfractalmedia2.5Fractionalintegralequationofbalanceofmomentum2.6Differentialequationsofbalanceofmomentum2.7Fractionalintegralequationofbalanceofenergy2.8Differentialequationofbalanceofenergy2.9Euler'sequationsforfractalmedia2.10Navier-Stokesequationsforfractalmedia2.11Equilibriumequationforfractalmedia2.12Bernoulliintegralforfractalmedia2.13Soundwavesinfractalmedia2.14One-dimensionalwaveequationinfractalmedia2.15ConclusionReferences3FraetalRigidBodyDynamics3.1Introduction3.2Fractionalequationformomentofinertia3.3Momentofinertiaoffractalrigidbodyball3.4Momentofinertiaforfractalrigidbodycylinder3.5Equationsofmotionforfractalrigidbody3.6Pendulumwithfractalrigidbody3.7Fractalrigidbodyrollingdownaninclinedplane3.8ConclusionReferences4ElectrodynamiesofFractalDistributionsofChargesandFields4.1Introduction4.2Electricchargeoffractaldistribution4.3Electriccurrentforfractaldistribution4.4Gauss'theoremforfractaldistribution4.5Stokes'theoremforfractaldistribution4.6Chargeconservationforfractaldistribution4.7Coulomb'sandBiot-Savartlawsforfractaldistribution...4.8Gauss'lawforfractaldistribution4.9Ampere'slawforfractaldistribution4.10IntegralMaxwellequationsforfractaldistribution4.11Fractaldistributionasaneffectivemedium4.12Electricmultipoleexpansionforfractaldistribution4.13Electricdipolemomentoffractaldistribution4.14Electricquadrupolemomentoffractaldistribution4.15Magnetohydrodynamicsoffractaldistribution4.16StationarystatesinmagnetohydrodynamicsoffractalDistributions4.17ConclusionReferences5Ginzburg-LandauEquationforFractalMedia5.1Introduction5.2Fractionalgeneralizationoffreeenergyfunctional5.3Ginzburg-Landauequationfromfreeenergyfunctional5.4Fractionalequationsfromvariationalequation5.5ConclusionReferences6Fokker-PlanckEquationforFractalDistributionsofProbability6.1Introduction6.2Fractionalequationforaveragevalues6.3FractionalChapman-Kolmogorovequation6.4Fokker-Planckequationforfractaldistribution6.5StationarysolutionsofgeneralizedFokker-Planckequation6.6Conclusion:References7StatisticalMechanicsofFractalPhaseSpaceDistributions7.1Introduction7.2Fractaldistributioninphasespace7.3Fractionalphasevolumeforconfigurationspace7.4Fractionalphasevolumeforphasespace7.5Fractionalgeneralizationofnormalizationcondition7.6Continuityequationforfractaldistributioninconfigurationspace.7.7Continuityequationforfractaldistributioninphasespace7.8Fractionalaveragevaluesforconfigurationspace7.9Fractionalaveragevaluesforphasespace7.10GeneralizedLiouvilleequation7.11Reduceddistributionfunctions7.12ConclusionReferencesPartⅡFractionalDynamicsandLong-RangeInteractions8FractionalDynamicsofMediawithLong-RangeInteraction8.1Introduction8.2Equationsoflatticevibrationsanddispersionlaw8.3Equationsofmotionforinteractingparticles8.4Transformoperationfordiscretemodels8.5Fourierseriestransformofequationsofmotion8.6Alpha-interactionofparticles8.7Fractionalspatialderivatives8.8Rieszfractionalderivativesandintegrals8.9Continuouslimitsofdiscreteequations8.10Linearnearest-neighborinteraction8.11Linearintegerlong-rangealpha-interaction8.12Linearfractionallong-rangealpha-interaction8.13Fractionalreaction-diffusionequation8.14Nonlinearlong-rangealpha-interaction8.15Fractional3-dimensionallatticeequation8.16Fractionalderivativesfromdispersionlaw8.17Fractallong-rangeinteraction8.18Fractaldispersionlaw8.19Grtinwald-Letnikov-Rieszlong-rangeinteraction8.20ConclusionReferences9FractionalGinzburg-LandauEquation9.1Introduction9.2ParticularsolutionoffractionalGinzburg-Landauequation...9.3Stabilityofplane-wavesolution9.4Forcedfractionalequation9.5ConclusionReferences10Psi-SeriesApproachtoFractionalEquations10.1Introduction10.2Singularbehavioroffractionalequation10.3Resonancetermsoffractionalequation10.4Psi-seriesforfractionalequationofrationalorder10.5Nexttosingularbehavior10.6ConclusionReferencesPartⅢFractionalSpatialDynamics11FractionalVectorCalculus11.1Introduction11.2Generalizationofvectorcalculus11.3Fundamentaltheoremoffractionalcalculus11.4Fractionaldifferentialvectoroperators11.5Fractionalintegralvectoroperations11.6FractionalGreen'sformula11.7FractionalStokes'formula11.8FractionalGauss'formula……PartⅣFractionalTemporalDynamicsPartⅤFractionalQuantumDynamicsIndex
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