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| Author | : Vasily E. Tarasov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 504 |
| Release | : 2011-01-04 |
| Genre | : Science |
| ISBN | : 3642140033 |
Download Fractional Dynamics Book in PDF, ePub and Kindle
"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.
| Author | : Carlo Cattani |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 392 |
| Release | : 2015-01-01 |
| Genre | : Mathematics |
| ISBN | : 3110472090 |
Download Fractional Dynamics Book in PDF, ePub and Kindle
The book is devoted to recent developments in the theory of fractional calculus and its applications. Particular attention is paid to the applicability of this currently popular research field in various branches of pure and applied mathematics. In particular, the book focuses on the more recent results in mathematical physics, engineering applications, theoretical and applied physics as quantum mechanics, signal analysis, and in those relevant research fields where nonlinear dynamics occurs and several tools of nonlinear analysis are required. Dynamical processes and dynamical systems of fractional order attract researchers from many areas of sciences and technologies, ranging from mathematics and physics to computer science.
| Author | : Dumitru Baleanu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 302 |
| Release | : 2011-11-19 |
| Genre | : Technology & Engineering |
| ISBN | : 1461404576 |
Download Fractional Dynamics and Control Book in PDF, ePub and Kindle
Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science.
| Author | : Thomas Michelitsch |
| Publisher | : John Wiley & Sons |
| Total Pages | : 340 |
| Release | : 2019-04-30 |
| Genre | : Technology & Engineering |
| ISBN | : 178630158X |
Download Fractional Dynamics on Networks and Lattices Book in PDF, ePub and Kindle
This book analyzes stochastic processes on networks and regular structures such as lattices by employing the Markovian random walk approach. Part 1 is devoted to the study of local and non-local random walks. It shows how non-local random walk strategies can be defined by functions of the Laplacian matrix that maintain the stochasticity of the transition probabilities. A major result is that only two types of functions are admissible: type (i) functions generate asymptotically local walks with the emergence of Brownian motion, whereas type (ii) functions generate asymptotically scale-free non-local “fractional” walks with the emergence of Lévy flights. In Part 2, fractional dynamics and Lévy flight behavior are analyzed thoroughly, and a generalization of Pólya's classical recurrence theorem is developed for fractional walks. The authors analyze primary fractional walk characteristics such as the mean occupation time, the mean first passage time, the fractal scaling of the set of distinct nodes visited, etc. The results show the improved search capacities of fractional dynamics on networks.
| Author | : Santanu Saha Ray |
| Publisher | : CRC Press |
| Total Pages | : 232 |
| Release | : 2015-07-29 |
| Genre | : Mathematics |
| ISBN | : 149872728X |
Download Fractional Calculus with Applications for Nuclear Reactor Dynamics Book in PDF, ePub and Kindle
Introduces Novel Applications for Solving Neutron Transport EquationsWhile deemed nonessential in the past, fractional calculus is now gaining momentum in the science and engineering community. Various disciplines have discovered that realistic models of physical phenomenon can be achieved with fractional calculus and are using them in numerous way
| Author | : Aleksei Tepljakov |
| Publisher | : Springer |
| Total Pages | : 184 |
| Release | : 2017-02-08 |
| Genre | : Technology & Engineering |
| ISBN | : 3319529501 |
Download Fractional-order Modeling and Control of Dynamic Systems Book in PDF, ePub and Kindle
This book reports on an outstanding research devoted to modeling and control of dynamic systems using fractional-order calculus. It describes the development of model-based control design methods for systems described by fractional dynamic models. More than 300 years had passed since Newton and Leibniz developed a set of mathematical tools we now know as calculus. Ever since then the idea of non-integer derivatives and integrals, universally referred to as fractional calculus, has been of interest to many researchers. However, due to various issues, the usage of fractional-order models in real-life applications was limited. Advances in modern computer science made it possible to apply efficient numerical methods to the computation of fractional derivatives and integrals. This book describes novel methods developed by the author for fractional modeling and control, together with their successful application in real-world process control scenarios.
| Author | : Vasily E. Tarasov |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 602 |
| Release | : 2021-01-18 |
| Genre | : Business & Economics |
| ISBN | : 3110627450 |
Download Economic Dynamics with Memory Book in PDF, ePub and Kindle
This book presents the applications of fractional calculus, fractional operators of non-integer orders and fractional differential equations in describing economic dynamics with long memory. Generalizations of basic economic concepts, notions and methods for the economic processes with memory are suggested. New micro and macroeconomic models with continuous time are proposed to describe the fractional economic dynamics with long memory as well.
| Author | : Joseph Klafter |
| Publisher | : World Scientific |
| Total Pages | : 530 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 9814340588 |
Download Fractional Dynamics Book in PDF, ePub and Kindle
This volume provides the latest developments in the field of fractional dynamics, which covers fractional (anomalous) transport phenomena, fractional statistical mechanics, fractional quantum mechanics and fractional quantum field theory. The contributors are selected based on their active and important contributions to their respective topics. This volume is the first of its kind that covers such a comprehensive range of topics in fractional dynamics. It will point out to advanced undergraduate and graduate students, and young researchers the possible directions of research in this subject. In addition to those who intend to work in this field and those already in the field, this volume will also be useful for researchers not directly involved in the field, but want to know the current status and trends of development in this subject. This latter group includes theoretical chemists, mathematical biologists and engineers.
| Author | : George M. Zaslavsky |
| Publisher | : Oxford University Press on Demand |
| Total Pages | : 436 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 0198526040 |
Download Hamiltonian Chaos and Fractional Dynamics Book in PDF, ePub and Kindle
This books gives a realistic contemporary image of Hamiltonian dynamics, dealing with the basic principles of the Hamiltonian theory of chaos in addition to very recent and unusual applications of nonlinear dynamics and the fractality of dynamics.
| Author | : Vasily E. Tarasov |
| Publisher | : MDPI |
| Total Pages | : 278 |
| Release | : 2020-06-03 |
| Genre | : Business & Economics |
| ISBN | : 303936118X |
Download Mathematical Economics Book in PDF, ePub and Kindle
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.
