Fractional Dynamics

Author: Vasily E. Tarasov
Publisher: Springer Science & Business Media
ISBN: 9783642140037
Release Date: 2011-01-04
Genre: Science

"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.

Advances in Harmonic Analysis and Operator Theory

Author: Alexandre Almeida
Publisher: Springer Science & Business Media
ISBN: 9783034805162
Release Date: 2013-01-31
Genre: Mathematics

This volume is dedicated to Professor Stefan Samko on the occasion of his seventieth birthday. The contributions display the range of his scientific interests in harmonic analysis and operator theory. Particular attention is paid to fractional integrals and derivatives, singular, hypersingular and potential operators in variable exponent spaces, pseudodifferential operators in various modern function and distribution spaces, as well as related applications, to mention but a few. Most contributions were firstly presented in two conferences at Lisbon and Aveiro, Portugal, in June‒July 2011.

Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness

Author: Józef Banaś
Publisher: Springer
ISBN: 9789811037221
Release Date: 2017-05-24
Genre: Mathematics

This book offers a comprehensive treatment of the theory of measures of noncompactness. It discusses various applications of the theory of measures of noncompactness, in particular, by addressing the results and methods of fixed-point theory. The concept of a measure of noncompactness is very useful for the mathematical community working in nonlinear analysis. Both these theories are especially useful in investigations connected with differential equations, integral equations, functional integral equations and optimization theory. Thus, one of the book’s central goals is to collect and present sufficient conditions for the solvability of such equations. The results are established in miscellaneous function spaces, and particular attention is paid to fractional calculus.

Local Fractional Integral Transforms and Their Applications

Author: Xiao Jun Yang
Publisher: Academic Press
ISBN: 9780128040324
Release Date: 2015-10-22
Genre: Mathematics

Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors. The methods of integral transforms via local fractional calculus have been used to solve various local fractional ordinary and local fractional partial differential equations and also to figure out the presence of the fractal phenomenon. The book presents the basics of the local fractional derivative operators and investigates some new results in the area of local integral transforms. Provides applications of local fractional Fourier Series Discusses definitions for local fractional Laplace transforms Explains local fractional Laplace transforms coupled with analytical methods

Fractional order Modeling of Nuclear Reactor From Subdiffusive Neutron Transport to Control oriented Models

Author: Vishwesh Vyawahare
Publisher: Springer
ISBN: 9789811075872
Release Date: 2018-02-03
Genre: Computers

This book addresses the topic of fractional-order modeling of nuclear reactors. Approaching neutron transport in the reactor core as anomalous diffusion, specifically subdiffusion, it starts with the development of fractional-order neutron telegraph equations. Using a systematic approach, the book then examines the development and analysis of various fractional-order models representing nuclear reactor dynamics, ultimately leading to the fractional-order linear and nonlinear control-oriented models. The book utilizes the mathematical tool of fractional calculus, the calculus of derivatives and integrals with arbitrary non-integer orders (real or complex), which has recently been found to provide a more compact and realistic representation to the dynamics of diverse physical systems. Including extensive simulation results and discussing important issues related to the fractional-order modeling of nuclear reactors, the book offers a valuable resource for students and researchers working in the areas of fractional-order modeling and control and nuclear reactor modeling.

Advances in Fractional Calculus

Author: J. Sabatier
Publisher: Springer Science & Business Media
ISBN: 9781402060427
Release Date: 2007-07-28
Genre: Mathematics

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.

Anomalous Transport

Author: Rainer Klages
Publisher: John Wiley & Sons
ISBN: 3527407227
Release Date: 2008-09-02
Genre: Science

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 the following fundamental aspects of anomalous transport: * Fractional calculus and stochastic theory * Dynamical systems and deterministic transport * Anomalous transport in disordered systems * Applications to complex systems and experimental results.

Advanced Research on Computer Science and Information Engineering

Author: Gang Shen
Publisher: Springer
ISBN: 9783642214110
Release Date: 2011-05-09
Genre: Computers

This two-volume set (CCIS 152 and CCIS 153) constitutes the refereed proceedings of the International Conference on Computer Science and Information Engineering, CSIE 2011, held in Zhengzhou, China, in May 2011. The 159 revised full papers presented in both volumes were carefully reviewed and selected from a large number of submissions. The papers present original research results that are broadly relevant to the theory and applications of Computer Science and Information Engineering and address a wide variety of topics such as algorithms, automation, artificial intelligence, bioinformatics, computer networks, computer security, computer vision, modeling and simulation, databases, data mining, e-learning, e-commerce, e-business, image processing, knowledge management, multimedia, mobile computing, natural computing, open and innovative education, pattern recognition, parallel computing, robotics, wireless networks, and Web applications.

Advanced Lasers

Author: Oleksiy Shulika
Publisher: Springer
ISBN: 9789401794817
Release Date: 2015-04-28
Genre: Technology & Engineering

Presenting a blend of applied and fundamental research in highly interdisciplinary subjects of rapidly developing areas, this book contains contributions on the frontiers and hot topics of laser physics, laser technology and laser engineering, and covers a wide range of laser topics, from all-optical signal processing and chaotic optical communication to production of superwicking surfaces, correction of extremely high-power beams, and generation of ultrabroadband spectra. It presents both review-type contributions and well researched and documented case studies, and is intended for graduate students, young scientist, and emeritus scientist working/studying in laser physics, optoelectronics, optics, photonics, and adjacent areas. The book contains both experimental and theoretical studies, as well as combinations of these two, which is known to be a most useful and interesting form of reporting scientific results, allowing students to really learn from each contribution. The book contains over 130 illustrations.

Mathematica for Theoretical Physics

Author: Gerd Baumann
Publisher: Springer Science & Business Media
ISBN: 0387251138
Release Date: 2006-01-16
Genre: Science

Class-tested textbook that shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica® to derive numeric and symbolic solutions. Delivers dozens of fully interactive examples for learning and implementation, constants and formulae can readily be altered and adapted for the user’s purposes. New edition offers enlarged two-volume format suitable to courses in mechanics and electrodynamics, while offering dozens of new examples and a more rewarding interactive learning environment.