© 2010

Fractional Dynamics

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


  • 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 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

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.


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

Authors and affiliations

  1. 1.Skobeltsyn Institute of Nuclear PhysicsMoscow State UniversityMoscowRussia

Bibliographic information

Industry Sectors
Finance, Business & Banking


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)