Verfügbarkeit: Fractional calculus in analysis, dynamics, and optimal control /

Fractional calculus in analysis, dynamics, and optimal control /:

This book is devoted to applications of fractional calculus in classical fields of mathematics like analysis, dynamics, partial differential equations and optimal control. The first chapter deals with the notion of local fractional derivatives and its applications to the study of regularity and geom...

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Bibliographische Detailangaben
Weitere Verfasser:	Cresson, Jacky (HerausgeberIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	New York : Nova Publishers, [2014]
Schriftenreihe:	Mathematics research developments series.
Schlagworte:	Fractional calculus. Dérivées fractionnaires. MATHEMATICS > Calculus. MATHEMATICS > Mathematical Analysis. Fractional calculus
Online-Zugang:	Volltext
Zusammenfassung:	This book is devoted to applications of fractional calculus in classical fields of mathematics like analysis, dynamics, partial differential equations and optimal control. The first chapter deals with the notion of local fractional derivatives and its applications to the study of regularity and geometry of curves. The second chapter develops the notion of fractional embedding and fractional assymetric calculus of variations in order to find fractional Lagrangian variational structures for classical dissipative partial differential equations. In continuation of this chapter, a fractional analog.
Beschreibung:	1 online resource.
Bibliographie:	Includes bibliographical references and index.
ISBN:	9781629486598 1629486590

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MARC


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505	0		\|a ""FRACTIONAL CALCULUS IN ANALYSIS, DYNAMICS AND OPTIMAL CONTROL""; ""FRACTIONAL CALCULUS IN ANALYSIS, DYNAMICS AND OPTIMAL CONTROL""; ""LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA""; ""CONTENTS""; ""PREFACE""; ""Chapter 1: LOCAL FRACTIONAL DERIVATIVES""; ""1. Introduction""; ""2. Non-differentiable and Non-analytic Functions""; ""3. Measure and Dimension""; ""4. Fractional Calculus""; ""5. Generalizations""; ""Acknowledgment""; ""References""; ""Chapter 2: FRACTIONAL VARIATIONAL EMBEDDING AND LAGRANGIAN FORMULATIONS OF DISSIPATIVE PARTIAL DIFFERENTIAL EQUATIONS""; ""1. Introduction""
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505	8		\|a ""3. Direct Methods""""4. Indirect Methods""; ""5. Conclusion""; ""Acknowledgments""; ""References""; ""INDEX""
520			\|a This book is devoted to applications of fractional calculus in classical fields of mathematics like analysis, dynamics, partial differential equations and optimal control. The first chapter deals with the notion of local fractional derivatives and its applications to the study of regularity and geometry of curves. The second chapter develops the notion of fractional embedding and fractional assymetric calculus of variations in order to find fractional Lagrangian variational structures for classical dissipative partial differential equations. In continuation of this chapter, a fractional analog.
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contents	""FRACTIONAL CALCULUS IN ANALYSIS, DYNAMICS AND OPTIMAL CONTROL""; ""FRACTIONAL CALCULUS IN ANALYSIS, DYNAMICS AND OPTIMAL CONTROL""; ""LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA""; ""CONTENTS""; ""PREFACE""; ""Chapter 1: LOCAL FRACTIONAL DERIVATIVES""; ""1. Introduction""; ""2. Non-differentiable and Non-analytic Functions""; ""3. Measure and Dimension""; ""4. Fractional Calculus""; ""5. Generalizations""; ""Acknowledgment""; ""References""; ""Chapter 2: FRACTIONAL VARIATIONAL EMBEDDING AND LAGRANGIAN FORMULATIONS OF DISSIPATIVE PARTIAL DIFFERENTIAL EQUATIONS""; ""1. Introduction"" ""2. Variational Principles and Dissipative Systems""""3. Embeddings Formalisms of ODEs and PDEs""; ""4. Asymmetric Fractional Embedding""; ""5. Fractional Variational Formulation of Dissipative Ordinary Differential Equations""; ""6. Variational Formulation of Dissipative Partial Differential Equations""; ""References""; ""Chapter 3: A CLASS OF FRACTIONAL OPTIMAL CONTROL PROBLEMS AND FRACTIONAL PONTRYAGINâ€?S SYSTEMS. VARIATIONAL INTEGRATOR AND EXISTENCE OF CONTINUOUS/DISCRETE NOETHERâ€?S THEOREMS""; ""Introduction""; ""1. A Class of Fractional Optimal Control Problems"" ""2. Variational Integrator for Fractional Pontryaginâ€?s Systems""""References""; ""Chapter 4: FRACTAL TRAPS AND FRACTIONAL DYNAMICS""; ""Abstract""; ""1. Introduction""; ""2. Studied System""; ""3. Construction of a Simple Model""; ""4. Dynamical Traps and Anomalous Diffusion""; ""5. Fractional Infinitesimal Generator""; ""6. Discussion""; ""7. Conclusion""; ""References""; ""Chapter 5: NUMERICAL APPROXIMATIONS TO FRACTIONAL PROBLEMS OF THE CALCULUS OF VARIATIONS AND OPTIMAL CONTROL""; ""1. Introduction""; ""2. Expansion Formulas to Approximate Fractional Derivatives"" ""3. Direct Methods""""4. Indirect Methods""; ""5. Conclusion""; ""Acknowledgments""; ""References""; ""INDEX""
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series2	Mathematics Research Developments
spelling	Fractional calculus in analysis, dynamics, and optimal control / Jacky Cresson, editor. New York : Nova Publishers, [2014] 1 online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier Mathematics Research Developments Includes bibliographical references and index. Description based on print version record. ""FRACTIONAL CALCULUS IN ANALYSIS, DYNAMICS AND OPTIMAL CONTROL""; ""FRACTIONAL CALCULUS IN ANALYSIS, DYNAMICS AND OPTIMAL CONTROL""; ""LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA""; ""CONTENTS""; ""PREFACE""; ""Chapter 1: LOCAL FRACTIONAL DERIVATIVES""; ""1. Introduction""; ""2. Non-differentiable and Non-analytic Functions""; ""3. Measure and Dimension""; ""4. Fractional Calculus""; ""5. Generalizations""; ""Acknowledgment""; ""References""; ""Chapter 2: FRACTIONAL VARIATIONAL EMBEDDING AND LAGRANGIAN FORMULATIONS OF DISSIPATIVE PARTIAL DIFFERENTIAL EQUATIONS""; ""1. Introduction"" ""2. Variational Principles and Dissipative Systems""""3. Embeddings Formalisms of ODEs and PDEs""; ""4. Asymmetric Fractional Embedding""; ""5. Fractional Variational Formulation of Dissipative Ordinary Differential Equations""; ""6. Variational Formulation of Dissipative Partial Differential Equations""; ""References""; ""Chapter 3: A CLASS OF FRACTIONAL OPTIMAL CONTROL PROBLEMS AND FRACTIONAL PONTRYAGINâ€?S SYSTEMS. VARIATIONAL INTEGRATOR AND EXISTENCE OF CONTINUOUS/DISCRETE NOETHERâ€?S THEOREMS""; ""Introduction""; ""1. A Class of Fractional Optimal Control Problems"" ""2. Variational Integrator for Fractional Pontryaginâ€?s Systems""""References""; ""Chapter 4: FRACTAL TRAPS AND FRACTIONAL DYNAMICS""; ""Abstract""; ""1. Introduction""; ""2. Studied System""; ""3. Construction of a Simple Model""; ""4. Dynamical Traps and Anomalous Diffusion""; ""5. Fractional Infinitesimal Generator""; ""6. Discussion""; ""7. Conclusion""; ""References""; ""Chapter 5: NUMERICAL APPROXIMATIONS TO FRACTIONAL PROBLEMS OF THE CALCULUS OF VARIATIONS AND OPTIMAL CONTROL""; ""1. Introduction""; ""2. Expansion Formulas to Approximate Fractional Derivatives"" ""3. Direct Methods""""4. Indirect Methods""; ""5. Conclusion""; ""Acknowledgments""; ""References""; ""INDEX"" This book is devoted to applications of fractional calculus in classical fields of mathematics like analysis, dynamics, partial differential equations and optimal control. The first chapter deals with the notion of local fractional derivatives and its applications to the study of regularity and geometry of curves. The second chapter develops the notion of fractional embedding and fractional assymetric calculus of variations in order to find fractional Lagrangian variational structures for classical dissipative partial differential equations. In continuation of this chapter, a fractional analog. English. Fractional calculus. http://id.loc.gov/authorities/subjects/sh93004015 Dérivées fractionnaires. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Fractional calculus fast Cresson, Jacky, editor. has work: Fractional Calculus in Analysis, Dynamics and Optimal Control (Text) https://id.oclc.org/worldcat/entity/E39PCXQJvHXfdGGdQW8m9tVPkP https://id.oclc.org/worldcat/ontology/hasWork Print version: Fractional calculus in analysis, dynamics, and optimal control New York : Nova Publishers, [2014] 1629486353 (hardcover) (DLC) 2013043481 Mathematics research developments series. http://id.loc.gov/authorities/names/no2009139785 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=714795 Volltext
spellingShingle	Fractional calculus in analysis, dynamics, and optimal control / Mathematics research developments series. ""FRACTIONAL CALCULUS IN ANALYSIS, DYNAMICS AND OPTIMAL CONTROL""; ""FRACTIONAL CALCULUS IN ANALYSIS, DYNAMICS AND OPTIMAL CONTROL""; ""LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA""; ""CONTENTS""; ""PREFACE""; ""Chapter 1: LOCAL FRACTIONAL DERIVATIVES""; ""1. Introduction""; ""2. Non-differentiable and Non-analytic Functions""; ""3. Measure and Dimension""; ""4. Fractional Calculus""; ""5. Generalizations""; ""Acknowledgment""; ""References""; ""Chapter 2: FRACTIONAL VARIATIONAL EMBEDDING AND LAGRANGIAN FORMULATIONS OF DISSIPATIVE PARTIAL DIFFERENTIAL EQUATIONS""; ""1. Introduction"" ""2. Variational Principles and Dissipative Systems""""3. Embeddings Formalisms of ODEs and PDEs""; ""4. Asymmetric Fractional Embedding""; ""5. Fractional Variational Formulation of Dissipative Ordinary Differential Equations""; ""6. Variational Formulation of Dissipative Partial Differential Equations""; ""References""; ""Chapter 3: A CLASS OF FRACTIONAL OPTIMAL CONTROL PROBLEMS AND FRACTIONAL PONTRYAGINâ€?S SYSTEMS. VARIATIONAL INTEGRATOR AND EXISTENCE OF CONTINUOUS/DISCRETE NOETHERâ€?S THEOREMS""; ""Introduction""; ""1. A Class of Fractional Optimal Control Problems"" ""2. Variational Integrator for Fractional Pontryaginâ€?s Systems""""References""; ""Chapter 4: FRACTAL TRAPS AND FRACTIONAL DYNAMICS""; ""Abstract""; ""1. Introduction""; ""2. Studied System""; ""3. Construction of a Simple Model""; ""4. Dynamical Traps and Anomalous Diffusion""; ""5. Fractional Infinitesimal Generator""; ""6. Discussion""; ""7. Conclusion""; ""References""; ""Chapter 5: NUMERICAL APPROXIMATIONS TO FRACTIONAL PROBLEMS OF THE CALCULUS OF VARIATIONS AND OPTIMAL CONTROL""; ""1. Introduction""; ""2. Expansion Formulas to Approximate Fractional Derivatives"" ""3. Direct Methods""""4. Indirect Methods""; ""5. Conclusion""; ""Acknowledgments""; ""References""; ""INDEX"" Fractional calculus. http://id.loc.gov/authorities/subjects/sh93004015 Dérivées fractionnaires. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Fractional calculus fast
subject_GND	http://id.loc.gov/authorities/subjects/sh93004015
title	Fractional calculus in analysis, dynamics, and optimal control /
title_auth	Fractional calculus in analysis, dynamics, and optimal control /
title_exact_search	Fractional calculus in analysis, dynamics, and optimal control /
title_full	Fractional calculus in analysis, dynamics, and optimal control / Jacky Cresson, editor.
title_fullStr	Fractional calculus in analysis, dynamics, and optimal control / Jacky Cresson, editor.
title_full_unstemmed	Fractional calculus in analysis, dynamics, and optimal control / Jacky Cresson, editor.
title_short	Fractional calculus in analysis, dynamics, and optimal control /
title_sort	fractional calculus in analysis dynamics and optimal control
topic	Fractional calculus. http://id.loc.gov/authorities/subjects/sh93004015 Dérivées fractionnaires. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Fractional calculus fast
topic_facet	Fractional calculus. Dérivées fractionnaires. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Fractional calculus
url	https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=714795
work_keys_str_mv	AT cressonjacky fractionalcalculusinanalysisdynamicsandoptimalcontrol

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