分数维动力学（国内英文版）

图书标准信息

• 作者 塔拉索夫（Vasily E.Tarasov）、罗朝俊、伊布拉基莫夫 著
• 出版社 高等教育出版社
• 出版时间 2010-08
• 版次 1
• ISBN 9787040294736
• 定价 89.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 504页
• 字数 780千字
• 正文语种 英语
• 丛书 非线性物理科学

【内容简介】

NonlinearPhysicalSciencefocusesontherecentadvancesoffundamentaltheoriesandprinciples，analyticalandsymbolicapproaches，aswellascomputationaltechniquesinnonlinearphysicalscienceandnonlinearmathematicswithengineeringapplications.

【目录】

PartIFractionfilContinuousModelsofFractalDistributions
1FractionalIntegrationandFractals
1.1Riemann-Liouvillefractionalintegrals
1.2Liouvillefractionalintegrals
1.3Rieszfractionalintegrals
1.4Metricandmeasurespaces
1.5Hausdorffmeasure
1.6Hausdorffdimensionandfractals
1.7Box-countingdimension
1.8Massdimensionoffractalsystems
1.9Elementarymodelsoffractaldistributions
1.10Functionsandintegralsonfractals
1.11Propertiesofintegralsonfractals
1.12Integrationovernon-integer-dimensionalspace
1.13Multi-variableintegrationonfractals
1.14Massdistributiononfractals
1.15DensityofstatesinEuclideanspace
1.16Fractionalintegralandmeasureontherealaxis
1.17Fractionalintegralandmassontherealaxis
1.18Massoffractalmedia
1.19Electricchargeoffractaldistribution
1.20Probabilityonfractals
1.21Fractaldistributionofparticles
References

2HydrodynamicsofFractalMedia
2.1Introduction
2.2Equationofbalanceofmass
2.3Totaltimederivativeoffractionalintegral
2.4Equationofcontinuityforfractalmedia
2.5Fractionalintegralequationofbalanceofmomentum
2.6Differentialequationsofbalanceofmomentum
2.7Fractionalintegralequationofbalanceofenergy
2.8Differentialequationofbalanceofenergy
2.9Euler'sequationsforfractalmedia
2.10Navier-Stokesequationsforfractalmedia
2.11Equilibriumequationforfractalmedia
2.12Bernoulliintegralforfractalmedia
2.13Soundwavesinfractalmedia
2.14One-dimensionalwaveequationinfractalmedia
2.15Conclusion
References

3FraetalRigidBodyDynamics
3.1Introduction
3.2Fractionalequationformomentofinertia
3.3Momentofinertiaoffractalrigidbodyball
3.4Momentofinertiaforfractalrigidbodycylinder
3.5Equationsofmotionforfractalrigidbody
3.6Pendulumwithfractalrigidbody
3.7Fractalrigidbodyrollingdownaninclinedplane
3.8Conclusion
References

4Electrodynamiesof
FractalDistributionsofChargesandFields
4.1Introduction
4.2Electricchargeoffractaldistribution
4.3Electriccurrentforfractaldistribution
4.4Gauss'theoremforfractaldistribution
4.5Stokes'theoremforfractaldistribution
4.6Chargeconservationforfractaldistribution
4.7Coulomb'sandBiot-Savartlawsforfractaldistribution...
4.8Gauss'lawforfractaldistribution
4.9Ampere'slawforfractaldistribution
4.10IntegralMaxwellequationsforfractaldistribution
4.11Fractaldistributionasaneffectivemedium
4.12Electricmultipoleexpansionforfractaldistribution
4.13Electricdipolemomentoffractaldistribution
4.14Electricquadrupolemomentoffractaldistribution
4.15Magnetohydrodynamicsoffractaldistribution
4.16Stationarystatesinmagnetohydrodynamicsoffractal
Distributions
4.17Conclusion
References

5Ginzburg-LandauEquationforFractalMedia
5.1Introduction
5.2Fractionalgeneralizationoffreeenergyfunctional
5.3Ginzburg-Landauequationfromfreeenergyfunctional
5.4Fractionalequationsfromvariationalequation
5.5Conclusion
References
6Fokker-PlanckEquationforFractalDistributionsofProbability
6.1Introduction
6.2Fractionalequationforaveragevalues
6.3FractionalChapman-Kolmogorovequation
6.4Fokker-Planckequationforfractaldistribution
6.5StationarysolutionsofgeneralizedFokker-Planckequation
6.6Conclusion:
References

7StatisticalMechanicsofFractalPhaseSpaceDistributions
7.1Introduction
7.2Fractaldistributioninphasespace
7.3Fractionalphasevolumeforconfigurationspace
7.4Fractionalphasevolumeforphasespace
7.5Fractionalgeneralizationofnormalizationcondition
7.6Continuityequationforfractaldistributioninconfigurationspace.
7.7Continuityequationforfractaldistributioninphasespace
7.8Fractionalaveragevaluesforconfigurationspace
7.9Fractionalaveragevaluesforphasespace
7.10GeneralizedLiouvilleequation
7.11Reduceddistributionfunctions
7.12Conclusion
References

PartⅡFractionalDynamicsandLong-RangeInteractions
8FractionalDynamicsofMediawithLong-RangeInteraction
8.1Introduction
8.2Equationsoflatticevibrationsanddispersionlaw
8.3Equationsofmotionforinteractingparticles
8.4Transformoperationfordiscretemodels
8.5Fourierseriestransformofequationsofmotion
8.6Alpha-interactionofparticles
8.7Fractionalspatialderivatives
8.8Rieszfractionalderivativesandintegrals
8.9Continuouslimitsofdiscreteequations
8.10Linearnearest-neighborinteraction
8.11Linearintegerlong-rangealpha-interaction
8.12Linearfractionallong-rangealpha-interaction
8.13Fractionalreaction-diffusionequation
8.14Nonlinearlong-rangealpha-interaction
8.15Fractional3-dimensionallatticeequation
8.16Fractionalderivativesfromdispersionlaw
8.17Fractallong-rangeinteraction
8.18Fractaldispersionlaw
8.19Grtinwald-Letnikov-Rieszlong-rangeinteraction
8.20Conclusion
References

9FractionalGinzburg-LandauEquation
9.1Introduction
9.2ParticularsolutionoffractionalGinzburg-Landauequation...
9.3Stabilityofplane-wavesolution
9.4Forcedfractionalequation
9.5Conclusion
References

10Psi-SeriesApproachtoFractionalEquations
10.1Introduction
10.2Singularbehavioroffractionalequation
10.3Resonancetermsoffractionalequation
10.4Psi-seriesforfractionalequationofrationalorder
10.5Nexttosingularbehavior
10.6Conclusion
References

PartⅢFractionalSpatialDynamics
11FractionalVectorCalculus
11.1Introduction
11.2Generalizationofvectorcalculus
11.3Fundamentaltheoremoffractionalcalculus
11.4Fractionaldifferentialvectoroperators
11.5Fractionalintegralvectoroperations
11.6FractionalGreen'sformula
11.7FractionalStokes'formula
11.8FractionalGauss'formula
……
PartⅣFractionalTemporalDynamics
PartⅤFractionalQuantumDynamics
Index