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Fractional Dynamics

Applications of Fractional Calculus to Dynamics of Particles, Fields and Media

  • Book
  • © 2010

Overview

Authors:
  1. Vasily E. Tarasov

    1. Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia

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  • Describes modern approaches and new results in fractional dynamics
  • Both self-contained and can be used as a teaching resource in fractional calculus and theory of fractals
  • Describes some modern applications of fractional calculus to complex physical systems and new results of recent years

Part of the book series: Nonlinear Physical Science (NPS)

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-xv
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  2. Fractional Continuous Models of Fractal Distributions

    1. Front Matter

      Pages 1-1
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    2. Fractional Integration and Fractals

      • Vasily E. Tarasov
      Pages 3-48

    3. Hydrodynamics of Fractal Media

      • Vasily E. Tarasov
      Pages 49-71

    4. Fractal Rigid Body Dynamics

      • Vasily E. Tarasov
      Pages 73-87

    5. Electrodynamics of Fractal Distributions of Charges and Fields

      • Vasily E. Tarasov
      Pages 89-113

    6. Ginzburg-Landau Equation for Fractal Media

      • Vasily E. Tarasov
      Pages 115-122

    7. Fokker-Planck Equation for Fractal Distributions of Probability

      • Vasily E. Tarasov
      Pages 123-133

    8. Statistical Mechanics of Fractal Phase Space Distributions

      • Vasily E. Tarasov
      Pages 135-150

  3. Fractional Dynamics and Long-Range Interactions

    1. Front Matter

      Pages 151-151
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    2. Fractional Dynamics of Media with Long-Range Interaction

      • Vasily E. Tarasov
      Pages 153-214

    3. Fractional Ginzburg-Landau Equation

      • Vasily E. Tarasov
      Pages 215-225

    4. Psi-Series Approach to Fractional Equations

      • Vasily E. Tarasov
      Pages 227-237

  4. Fractional Spatial Dynamics

    1. Front Matter

      Pages 239-239
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    2. Fractional Vector Calculus

      • Vasily E. Tarasov
      Pages 241-264

    3. Fractional Exterior Calculus and Fractional Differential Forms

      • Vasily E. Tarasov
      Pages 265-291

    4. Fractional Dynamical Systems

      • Vasily E. Tarasov
      Pages 293-313

    5. Fractional Calculus of Variations in Dynamics

      • Vasily E. Tarasov
      Pages 315-333

    6. Fractional Statistical Mechanics

      • Vasily E. Tarasov
      Pages 335-353

  5. Fractional Temporal Dynamics

    1. Front Matter

      Pages 355-355
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Keywords

About this book

"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and an Associate Professor at Applied Mathematics and Physics Department of Moscow Aviation Institute.

Reviews

From the reviews:

“A scientific and reference guide for advanced researchers actively working in the field of chaos theory, wave dynamics, nonlinear dynamics and electromagnetic phenomena in media. It will be helpful for graduate students … who are looking for theoretical models to study complex dynamical systems under the influence of long-memory temporal and long-range spatial interactions. For those who are not engaged in the field but seeking new theoretical approaches and frameworks, the book will bring a variety of mathematical methods and tools involving fractional calculus.” (Nick Laskin, Mathematical Reviews, Issue 2012 f)

Authors and Affiliations

  • Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia

    Vasily E. Tarasov

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