1 Fractional Integration and Fractals

Fractional Dynamics: Applications of Fra 作者：Vasily E. Tarasov　　 ISBN：978-7-04-029473-6　出版时间：2010-08-20

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目录

Front Matter

Part I Fractional Continuous Models of Fractal Distributions

1 Fractional Integration and Fractals

2 Hydrodynamics of Fractal Media

3 Fractal Rigid Body Dynamics

4 Electrodynamics of Fractal Distributions of Charges and Fields

5 Ginzburg-Landau Equation for Fractal Media

6 Fokker-Planck Equation for Fractal Distributions of Probability

7 Statistical Mechanics of Fractal Phase Space Distributions

Part II Fractional Dynamics and Long-Range Interactions

8 Fractional Dynamics of Media with Long-Range Interaction

9 Fractional Ginzburg-Landau Equation

10 Psi-Series Approach to Fractional Equations

Part III Fractional Spatial Dynamics

11 Fractional Vector Calculus

12 Fractional Exterior Calculus and Fractional Differential Forms

13 Fractional Dynamical Systems

14 Fractional Calculus of Variations in Dynamics

15 Fractional Statistical Mechanics

Part IV Fractional Temporal Dynamics

16 Fractional Temporal Electrodynamics

17 Fractional Nonholonomic Dynamics

18 Fractional Dynamics and Discrete Maps with Memory

Part V Fractional Quantum Dynamics

19 Fractional Dynamics of Hamiltonian Quantum Systems

20 Fractional Dynamics of Open Quantum Systems

21 Quantum Analogs of Fractional Derivatives

Index

Nonlinear Physical Science
- 1.1 Riemann-Liouville fractional integrals
- 1.2 Liouville fractional integrals
- 1.3 Riesz fractional integrals
- 1.4 Metric and measure spaces
- 1.5 Hausdorff measure
- 1.6 Hausdorff dimension and fractals
- 1.7 Box-counting dimension
- 1.8 Mass dimension of fractal systems
- 1.9 Elementary models of fractal distributions
- 1.10 Functions and integrals on fractals
- 1.11 Properties of integrals on fractals
- 1.12 Integration over non-integer-dimensional space
- 1.13 Multi-variable integration on fractals
- 1.14 Mass distribution on fractals
- 1.15 Density of states in Euclidean space
- 1.16 Fractional integral and measure on the real axis
- 1.17 Fractional integral and mass on the real axis
- 1.18 Mass of fractal media
- 1.19 Electric charge of fractal distribution
- 1.20 Probability on fractals
- 1.21 Fractal distribution of particles
- References

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