一個運動質(zhì)點位置函數(shù)的一階導(dǎo)數(shù)表示速度，二階導(dǎo)數(shù)表示加速度，那么分數(shù)階導(dǎo)數(shù)的物理意義又是什么呢？分數(shù)階導(dǎo)數(shù)是因何而產(chǎn)生，它對現(xiàn)代分析學在物理學的應(yīng)用產(chǎn)生什么沖擊，在將來又有什么發(fā)展？《物理及工程中的分數(shù)維微積分》二卷本將為你提供一個詳細詮釋。
《物理及工程中的分數(shù)維微積分（第1卷）：數(shù)學基礎(chǔ)及其理論》介紹分數(shù)維微積分的數(shù)學基礎(chǔ)和相應(yīng)的理論，為這個現(xiàn)代分析學中的重要分支提供了詳細而又清晰的分析與介紹。
Part Ⅰ Background
1 Heredity and Nonlocality
1.1 Heredity
1.1.1 Concept of heredity
1.1.2 A short excursus in history
1.2 Volterra's heredity theory
1.2.1 Volterra's heredity laws
1.2.2 Hereditary string
1.2.3 Hereditarv oscillator
1.2.4 Energv drinciple
1.2.5 Hereditary electrodynamics
1.3 Hereditary kinetics
1.3.1 Mechanical origin of heredity
1.3.2 Hereditary Boltzmann equation
1.3.3 Fokker-Planckequation
Part Ⅰ Background
1 Heredity and Nonlocality
1.1 Heredity
1.1.1 Concept of heredity
1.1.2 A short excursus in history
1.2 Volterra's heredity theory
1.2.1 Volterra's heredity laws
1.2.2 Hereditary string
1.2.3 Hereditarv oscillator
1.2.4 Energv drinciple
1.2.5 Hereditary electrodynamics
1.3 Hereditary kinetics
1.3.1 Mechanical origin of heredity
1.3.2 Hereditary Boltzmann equation
1.3.3 Fokker-Planckequation
1.3.4 Pauli and Van Hove equations
1.3.5 Hybrid kinetic equations
1.4 Hereditary hydrodynamics
1.4.1 Physicalmotivation
1.4.2 Polymeric liquids
1.4.3 Turbulent diffusion
1.4.4 Coarse-grained diffusion models
1.5 Hereditarv viscoelasticity
1.5.1 Boltzmann's viscoelasticity model
1.5.2 Elastic solid： a mesoscopic approach
1.5.3 One-dimensional harmonic lattice
1.5.4 Axiomatic approach to continuum mechanics
1.6 Hereditary thermodynanucs
1.6.1 Mechanical approach
1.6.2 Hereditary heat-transfer
1.6.3 Extendedirreversible thermodynamics
1.6.4 Axiomatic approach
1.6.5 Ecology and climatology
1.7 Nonlocal models
1.7.1 Many-electron atoms
1.7.2 Electron correlation in metals
1.7.3 Plasma
1.7.4 Vlasov's nonlocal statistical mechanics
1.7.5 Turbulence
1.7.6 Aggregation equations
1.7.7 Nonlocal models in nano-plasticity
1.7.8 Nonlocal wave equations
References
2 Selfsinularity
2.1 Power functions
2.1.1 Standard power function
2.1.2 Properties ofpower functions
2.1.3 Memory
2.1.4 Fractals
2.2 Hydrodynamics
2.2.1 Newtonian fluids
2.2.2 Turbulence
2.2.3 Microscopic fluctuations
2.2.4 Non-Newtonian fiuids
2.3 Polymers
2.3.1 The Nutting law
2.3.2 Relaxation ofpolymer chains
2.3.3 Interpenetrating polymer networks
2.4 Reaction-diffusion
2.4.1 Diffusion
2.4.2 Polymerization
2.4.3 Coagulation and fragmentation
2.5 Solids
2.5.1 Dielectrics
2.5.2 Semiconductors
2.5.3 Spinglasses
2.5.4 Jonscher's universal relaxation law
2.6 Optics
2.6.1 Luminescence decay
2.6.2 Anomalous exciton kinetics
2.6.3 Blinking fluorescence of quantum dots
2.7 Geophysics
2.7.1 Atmosphere and ocean turbulence
……
PartⅡ Theory
Index
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