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.

Basic Theory

Author: Anatoly Kochubei
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 9783110570632
Release Date: 2019-02-19
Genre: Mathematics

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.

Applications in Engineering Life and Social Sciences

Author: Dumitru Bǎleanu
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 9783110571929
Release Date: 2019-04-01
Genre: Mathematics

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 eighth volume collects authoritative chapters covering several applications of fractional calculus in engineering, life and social sciences, including applications in signal and image analysis, and chaos.

Applications in Physics

Author: Vasily E. Tarasov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 9783110571004
Release Date: 2019-02-19
Genre: Mathematics

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.

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 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.

Bernhard Riemann s Gesammelte Mathematische Werke Und Wissenschaftlicher Nachlass

Author: Bernhard Riemann
Publisher: Wentworth Press
ISBN: 0341348635
Release Date: 2018-08-09
Genre: History

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Differentialgleichungen und ihre Anwendungen

Author: Martin Braun
Publisher: Springer-Verlag
ISBN: 9783642973413
Release Date: 2013-03-13
Genre: Mathematics

Dieses richtungsweisende Lehrbuch für die Anwendung der Mathematik in anderen Wissenschaftszweigen gibt eine Einführung in die Theorie der gewöhnlichen Differentialgleichungen. Fortran und APL-Programme geben den Studenten die Möglichkeit, verschiedene numerische Näherungsverfahren an ihrem PC selbst durchzurechnen. Aus den Besprechungen: "Die Darstellung ist überall mathematisch streng und zudem ungemein anregend. Abgesehen von manchen historischen Bemerkungen ... tragen dazu die vielen mit ausführlichem Hintergrund sehr eingehend entwickelten praktischen Anwendungen bei. ... Besondere Aufmerksamkeit wird der physikalisch und technisch so wichtigen Frage nach Stabilität von Lösungen eines Systems von Differentialgleichungen gewidmet. Das Buch ist wegen seiner geringen Voraussetzungen und vorzüglichen Didaktik schon für alle Studenten des 3. Semesters geeignet; seine eminent praktische Haltung empfiehlt es aber auch für alle Physiker, die mit Differentialgleichungen und ihren Anwendungen umzugehen haben." #Physikalische Blätter#

Fraktale Geometrie

Author: Kenneth J. Falconer
Publisher: Spektrum Akademischer Verlag
ISBN: 3860250752
Release Date: 1993-01-01
Genre:


Stochastik

Author: David Meintrup
Publisher: Springer-Verlag
ISBN: 9783540267072
Release Date: 2006-03-30
Genre: Mathematics

Fundierte und anwendungsbezogene Einführung in die Wahrscheinlichkeitstheorie und Statistik. Ob digitale Nachrichtenübertragung, Schaltkreissimulation, Verfahrenstechnik oder Financial Engineering - die meisten modernen Verfahren in der Technik und Informatik beruhen auf stochastischen Prinzipien. Alle Resultate sind in diesem Buch ausführlich motiviert und exakt bewiesen. Hervorragend geeignet für Selbststudium und Vorlesungsbegleitung.