Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media (Nonlinear Physical Science)

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. Front Matter....Pages i-xv Front Matter....Pages 1-1 Fractional Integration and Fractals....Pages 3-48 Hydrodynamics of Fractal Media....Pages 49-71 Fractal Rigid Body Dynamics....Pages 73-87 Electrodynamics of Fractal Distributions of Charges and Fields....Pages 89-113 Ginzburg-Landau Equation for Fractal Media....Pages 115-122 Fokker-Planck Equation for Fractal Distributions of Probability....Pages 123-133 Statistical Mechanics of Fractal Phase Space Distributions....Pages 135-150 Front Matter....Pages 151-151 Fractional Dynamics of Media with Long-Range Interaction....Pages 153-214 Fractional Ginzburg-Landau Equation....Pages 215-225 Psi-Series Approach to Fractional Equations....Pages 227-237 Front Matter....Pages 239-239 Fractional Vector Calculus....Pages 241-264 Fractional Exterior Calculus and Fractional Differential Forms....Pages 265-291 Fractional Dynamical Systems....Pages 293-313 Fractional Calculus of Variations in Dynamics....Pages 315-333 Fractional Statistical Mechanics....Pages 335-353 Front Matter....Pages 355-355 Fractional Temporal Electrodynamics....Pages 357-376 Fractional Nonholonomic Dynamics....Pages 377-408 Fractional Dynamics and Discrete Maps with Memory....Pages 409-453 Front Matter....Pages 455-455 Fractional Dynamics of Hamiltonian Quantum Systems....Pages 457-466 Fractional Dynamics of Open Quantum Systems....Pages 467-490 Front Matter....Pages 455-455 Quantum Analogs of Fractional Derivatives....Pages 491-502 Back Matter....Pages 503-505 Fractional Dynamics presents applications of fractional calculus, integral and differential equations of non-integer orders, and fractal properties. Written for scientists and graduate students alike, this volume is applicable to mechanics and applied mathematics, electrodynamics, quantum dynamics, and more.