Fractional Dynamics
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Fractional Dynamics
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Author : Vasily E. Tarasov
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-04
Fractional Dynamics written by Vasily E. Tarasov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-04 with Science categories.
"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 Dynamics
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Author : Carlo Cattani
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2015-01-01
Fractional Dynamics written by Carlo Cattani and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-01 with Mathematics categories.
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.
Hamiltonian Chaos And Fractional Dynamics
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Author : George M. Zaslavsky
language : en
Publisher: OUP Oxford
Release Date : 2004-12-23
Hamiltonian Chaos And Fractional Dynamics written by George M. Zaslavsky and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-23 with Mathematics categories.
The dynamics of realistic Hamiltonian systems has unusual microscopic features that are direct consequences of its fractional space-time structure and its phase space topology. The book deals with the fractality of the chaotic dynamics and kinetics, and also includes material on non-ergodic and non-well-mixing Hamiltonian dynamics. The book does not follow the traditional scheme of most of today's literature on chaos. The intention of the author has been to put together some of the most complex and yet open problems on the general theory of chaotic systems. The importance of the discussed issues and an understanding of their origin should inspire students and researchers to touch upon some of the deepest aspects of nonlinear dynamics. The book considers the basic principles of the Hamiltonian theory of chaos and some applications including for example, the cooling of particles and signals, control and erasing of chaos, polynomial complexity, Maxwell's Demon, and others. It presents a new and realistic image of the origin of dynamical chaos and randomness. An understanding of the origin of randomness in dynamical systems, which cannot be of the same origin as chaos, provides new insights in the diverse fields of physics, biology, chemistry, and engineering.
Fractional Dynamics And Control
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Author : Dumitru Baleanu
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-19
Fractional Dynamics And Control written by Dumitru Baleanu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-19 with Technology & Engineering categories.
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.
Fractional Order Nonlinear Systems
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Author : Ivo Petráš
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-30
Fractional Order Nonlinear Systems written by Ivo Petráš and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-30 with Technology & Engineering categories.
"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. Ivo Petráš is an Associate Professor of automatic control and the Director of the Institute of Control and Informatization of Production Processes, Faculty of BERG, Technical University of Košice, Slovak Republic. His main research interests include control systems, industrial automation, and applied mathematics.
Fractional Dynamics On Networks And Lattices
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Author : Thomas Michelitsch
language : en
Publisher: John Wiley & Sons
Release Date : 2019-04-30
Fractional Dynamics On Networks And Lattices written by Thomas Michelitsch and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-30 with Technology & Engineering categories.
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.
Fractional Order Analysis
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Author : Hemen Dutta
language : en
Publisher: John Wiley & Sons
Release Date : 2020-09-01
Fractional Order Analysis written by Hemen Dutta and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-01 with Mathematics categories.
A guide to the new research in the field of fractional order analysis Fractional Order Analysis contains the most recent research findings in fractional order analysis and its applications. The authors—noted experts on the topic—offer an examination of the theory, methods, applications, and the modern tools and techniques in the field of fractional order analysis. The information, tools, and applications presented can help develop mathematical methods and models with better accuracy. Comprehensive in scope, the book covers a range of topics including: new fractional operators, fractional derivatives, fractional differential equations, inequalities for different fractional derivatives and fractional integrals, fractional modeling related to transmission of Malaria, and dynamics of Zika virus with various fractional derivatives, and more. Designed to be an accessible text, several useful, relevant and connected topics can be found in one place, which is crucial for an understanding of the research problems of an applied nature. This book: Contains recent development in fractional calculus Offers a balance of theory, methods, and applications Puts the focus on fractional analysis and its interdisciplinary applications, such as fractional models for biological models Helps make research more relevant to real-life applications Written for researchers, professionals and practitioners, Fractional Order Analysis offers a comprehensive resource to fractional analysis and its many applications as well as information on the newest research.
Fractional Order Systems
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Author : Ahmad Taher Azar
language : en
Publisher: Academic Press
Release Date : 2018-08-16
Fractional Order Systems written by Ahmad Taher Azar and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-16 with Technology & Engineering categories.
Fractional Order Systems: Optimization, Control, Circuit Realizations and Applications consists of 21 contributed chapters by subject experts. Chapters offer practical solutions and novel methods for recent research problems in the multidisciplinary applications of fractional order systems, such as FPGA, circuits, memristors, control algorithms, photovoltaic systems, robot manipulators, oscillators, etc. This book is ideal for researchers working in the modeling and applications of both continuous-time and discrete-time dynamics and chaotic systems. Researchers from academia and industry who are working in research areas such as control engineering, electrical engineering, mechanical engineering, computer science, and information technology will find the book most informative. - Discusses multi-disciplinary applications with new fundamentals, modeling, analysis, design, realization and experimental results - Includes new circuits and systems based on the new nonlinear elements - Covers most of the linear and nonlinear fractional-order theorems that will solve many scientific issues for researchers - Closes the gap between theoretical approaches and real-world applications - Provides MATLAB® and Simulink code for many of the applications in the book
Theory And Applications Of Fractional Differential Equations
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Author : A.A. Kilbas
language : en
Publisher: Elsevier
Release Date : 2006-02-16
Theory And Applications Of Fractional Differential Equations written by A.A. Kilbas and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-16 with Mathematics categories.
This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.