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"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.

Fractional calculus --- Dynamics --- Engineering & Applied Sciences --- Mathematics --- Physics --- Physical Sciences & Mathematics --- Calculus --- Atomic Physics --- Applied Mathematics --- Applied Physics --- Fractional calculus. --- Dynamics. --- Dynamical systems --- Kinetics --- Derivatives and integrals, Fractional --- Differentiation of arbitrary order, Integration and --- Differintegration, Generalized --- Fractional derivatives and integrals --- Generalized calculus --- Generalized differintegration --- Integrals, Fractional derivatives and --- Integration and differentiation of arbitrary order --- Physics. --- Applied mathematics. --- Engineering mathematics. --- Calculus of variations. --- Statistical physics. --- Dynamical systems. --- Statistical Physics, Dynamical Systems and Complexity. --- Applications of Mathematics. --- Calculus of Variations and Optimal Control; Optimization. --- Theoretical, Mathematical and Computational Physics. --- Appl.Mathematics/Computational Methods of Engineering. --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Mathematics. --- Mathematical optimization. --- Complex Systems. --- Mathematical and Computational Engineering. --- Statistical Physics and Dynamical Systems. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Math --- Science --- Mathematical statistics --- Engineering --- Engineering analysis --- Statistical methods --- Mathematical physics. --- Physical mathematics --- Isoperimetrical problems --- Variations, Calculus of --- System theory. --- Calculus of Variations and Optimization. --- Mathematical and Computational Engineering Applications. --- Data processing. --- Systems, Theory of --- Systems science --- Philosophy

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"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.

Functional analysis --- Numerical methods of optimisation --- Discrete mathematics --- Mathematical statistics --- Mathematics --- Mathematical physics --- Classical mechanics. Field theory --- Statistical physics --- Applied physical engineering --- Engineering sciences. Technology --- Computer. Automation --- ICT (informatie- en communicatietechnieken) --- analyse (wiskunde) --- toegepaste wiskunde --- grafentheorie --- theoretische fysica --- economie --- statistiek --- wiskunde --- ingenieurswetenschappen --- fysica --- kansrekening --- dynamica --- optimalisatie

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This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus.

mathematical economics --- economic theory --- fractional calculus --- fractional dynamics --- long memory --- non-locality --- fractional generalization --- econometric modelling --- identification --- Phillips curve --- Mittag-Leffler function --- generalized fractional derivatives --- growth equation --- Mittag–Leffler function --- Caputo fractional derivative --- economic growth model --- least squares method --- fractional diffusion equation --- fundamental solution --- option pricing --- risk sensitivities --- portfolio hedging --- business cycle model --- stability --- time delay --- time-fractional-order --- Hopf bifurcation --- Einstein’s evolution equation --- Kolmogorov–Feller equation --- diffusion equation --- self-affine stochastic fields --- random market hypothesis --- efficient market hypothesis --- fractal market hypothesis --- financial time series analysis --- evolutionary computing --- modelling --- economic growth --- prediction --- Group of Twenty --- pseudo-phase space --- economy --- system modeling --- deep assessment --- least squares --- modeling --- GDP per capita --- LSTM --- econophysics --- continuous-time random walk (CTRW) --- Mittag–Leffler functions --- Laplace transform --- Fourier transform --- n/a --- Einstein's evolution equation --- Kolmogorov-Feller equation --- Mittag-Leffler functions

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This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus.

Economics, finance, business & management --- mathematical economics --- economic theory --- fractional calculus --- fractional dynamics --- long memory --- non-locality --- fractional generalization --- econometric modelling --- identification --- Phillips curve --- Mittag-Leffler function --- generalized fractional derivatives --- growth equation --- Caputo fractional derivative --- economic growth model --- least squares method --- fractional diffusion equation --- fundamental solution --- option pricing --- risk sensitivities --- portfolio hedging --- business cycle model --- stability --- time delay --- time-fractional-order --- Hopf bifurcation --- Einstein's evolution equation --- Kolmogorov-Feller equation --- diffusion equation --- self-affine stochastic fields --- random market hypothesis --- efficient market hypothesis --- fractal market hypothesis --- financial time series analysis --- evolutionary computing --- modelling --- economic growth --- prediction --- Group of Twenty --- pseudo-phase space --- economy --- system modeling --- deep assessment --- least squares --- modeling --- GDP per capita --- LSTM --- econophysics --- continuous-time random walk (CTRW) --- Mittag-Leffler functions --- Laplace transform --- Fourier transform

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