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Fractional Dynamics

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

  • Vasily E. Tarasov

Part of the Nonlinear Physical Science book series (NPS, volume 0)

Table of contents

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

    1. Front Matter
      Pages 1-1
    2. Vasily E. Tarasov
      Pages 3-48
    3. Vasily E. Tarasov
      Pages 49-71
    4. Vasily E. Tarasov
      Pages 73-87
    5. Vasily E. Tarasov
      Pages 115-122
  3. Fractional Dynamics and Long-Range Interactions

    1. Front Matter
      Pages 151-151
    2. Vasily E. Tarasov
      Pages 215-225
    3. Vasily E. Tarasov
      Pages 227-237
  4. Fractional Spatial Dynamics

    1. Front Matter
      Pages 239-239
    2. Vasily E. Tarasov
      Pages 241-264
    3. Vasily E. Tarasov
      Pages 293-313
    4. Vasily E. Tarasov
      Pages 315-333
    5. Vasily E. Tarasov
      Pages 335-353
  5. Fractional Temporal Dynamics

    1. Front Matter
      Pages 355-355
    2. Vasily E. Tarasov
      Pages 357-376
    3. Vasily E. Tarasov
      Pages 377-408
    4. Vasily E. Tarasov
      Pages 409-453
  6. Fractional Quantum Dynamics

    1. Front Matter
      Pages 455-455
    2. Vasily E. Tarasov
      Pages 457-466
    3. Vasily E. Tarasov
      Pages 467-490
    4. Vasily E. Tarasov
      Pages 491-502
  7. Back Matter
    Pages 503-505

About this book

Introduction

"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.

Keywords

Fokker-Planck equation Fractional Calculus Fractional Dynamics HEP Long-range Dynamical Systems NPS linear optimization nonlinear dynamics

Authors and affiliations

  • Vasily E. Tarasov
    • 1
  1. 1.Skobeltsyn Institute of Nuclear PhysicsMoscow State UniversityMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-14003-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-642-14002-0
  • Online ISBN 978-3-642-14003-7
  • Series Print ISSN 1867-8440
  • Buy this book on publisher's site