‘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.
Mục lục
Fractional Continuous Models of Fractal Distributions.- Fractional Integration and Fractals.- Hydrodynamics of Fractal Media.- Fractal Rigid Body Dynamics.- Electrodynamics of Fractal Distributions of Charges and Fields.- Ginzburg-Landau Equation for Fractal Media.- Fokker-Planck Equation for Fractal Distributions of Probability.- Statistical Mechanics of Fractal Phase Space Distributions.- Fractional Dynamics and Long-Range Interactions.- Fractional Dynamics of Media with Long-Range Interaction.- Fractional Ginzburg-Landau Equation.- Psi-Series Approach to Fractional Equations.- Fractional Spatial Dynamics.- Fractional Vector Calculus.- Fractional Exterior Calculus and Fractional Differential Forms.- Fractional Dynamical Systems.- Fractional Calculus of Variations in Dynamics.- Fractional Statistical Mechanics.- Fractional Temporal Dynamics.- Fractional Temporal Electrodynamics.- Fractional Nonholonomic Dynamics.- Fractional Dynamics and Discrete Maps with Memory.- Fractional Quantum Dynamics.- Fractional Dynamics of Hamiltonian Quantum Systems.- Fractional Dynamics of Open Quantum Systems.- Quantum Analogs of Fractional Derivatives.
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