Fractional Dynamics

Applications of Fractional Calculus to Dynamics of Particles, Fields and Media

Author: Vasily E. Tarasov

Publisher: Springer Science & Business Media

ISBN: 3642140033

Category: Science

Page: 505

View: 1181

DOWNLOAD NOW »

"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.
Release

Basic Theory

Author: Anatoly Kochubei,Yuri Luchko

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110571625

Category: Mathematics

Page: 489

View: 3448

DOWNLOAD NOW »

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.
Release

Fractional Calculus with Applications in Mechanics

Vibrations and Diffusion Processes

Author: Teodor M. Atanackovic,Stevan Pilipovic,Bogoljub Stankovic,Dusan Zorica

Publisher: John Wiley & Sons

ISBN: 1118577469

Category: Mathematics

Page: 336

View: 4403

DOWNLOAD NOW »

This book contains mathematical preliminaries in which basic definitions of fractional derivatives and spaces are presented. The central part of the book contains various applications in classical mechanics including fields such as: viscoelasticity, heat conduction, wave propagation and variational Hamilton–type principles. Mathematical rigor will be observed in the applications. The authors provide some problems formulated in the classical setting and some in the distributional setting. The solutions to these problems are presented in analytical form and these solutions are then analyzed numerically. Theorems on the existence of solutions will be presented for all examples discussed. In using various constitutive equations the restrictions following from the second law of thermodynamics will be implemented. Finally, the physical implications of obtained solutions will be discussed in detail.
Release

Applications in Physics

Author: Vasily E. Tarasov

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110571706

Category: Mathematics

Page: 314

View: 7055

DOWNLOAD NOW »

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This fourth volume collects authoritative chapters covering several applications of fractional calculus in physics, including classical and continuum mechanics.
Release

Advances in Fractional Calculus

Theoretical Developments and Applications in Physics and Engineering

Author: J. Sabatier,O. P. Agrawal,J. A. Tenreiro Machado

Publisher: Springer Science & Business Media

ISBN: 1402060424

Category: Mathematics

Page: 552

View: 6539

DOWNLOAD NOW »

In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.
Release

Anomalous Transport

Foundations and Applications

Author: Rainer Klages,Günter Radons,Igor M. Sokolov

Publisher: John Wiley & Sons

ISBN: 9783527407224

Category: Science

Page: 608

View: 5824

DOWNLOAD NOW »

This multi-author reference work provides a unique introduction to the currently emerging, highly interdisciplinary field of those transport processes that cannot be described by using standard methods of statistical mechanics. It comprehensively summarizes topics ranging from mathematical foundations of anomalous dynamics to the most recent experiments in this field. In so doing, this monograph extracts and emphasizes common principles and methods from many different disciplines while providing up-to-date coverage of this new field of research, considering such diverse applications as plasma physics, glassy material, cell science, and socio-economic aspects. The book will be of interest to both theorists and experimentalists in nonlinear dynamics, statistical physics and stochastic processes. It also forms an ideal starting point for graduate students moving into this area. 18 chapters written by internationally recognized experts in this field provide in-depth introductions to fundamental aspects of anomalous transport.
Release

Frontiers of Manufacturing and Design Science II

Author: Dong Ye Sun,Wen Pei Sung,Ran Chen

Publisher: Trans Tech Publications Ltd

ISBN: 3038137154

Category: Technology & Engineering

Page: 5440

View: 1516

DOWNLOAD NOW »

Volume is indexed by Thomson Reuters CPCI-S (WoS). This collection of 949 peer-reviewed papers on the Frontiers of Manufacturing and Design Science is intended to promote the development of Manufacturing, Design and Materials Science, the strengthening of international academic cooperation and communications and the exchange of research ideas. This book provides readers with a broad overview of the latest advances in the field of Manufacturing and Design Science.
Release