Fractional calculus in analysis, dynamics, and optimal control / Jacky Cresson, editor.

Format:

Book

Contributor:

Cresson, Jacky, editor.

Series:

Mathematics research developments series.

Mathematics Research Developments

Language:

English

Subjects (All):

Fractional calculus.

Physical Description:

1 online resource (254 p.)

Place of Publication:

New York : Nova Science Publishers, Inc., 2014.

Language Note:

English

Summary:

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

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 PONTRYAGIN�S SYSTEMS. VARIATIONAL INTEGRATOR AND EXISTENCE OF CONTINUOUS/DISCRETE NOETHER�S THEOREMS""; ""Introduction""; ""1. A Class of Fractional Optimal Control Problems""

""2. Variational Integrator for Fractional Pontryagin�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""

Notes:

Description based upon print version of record.

Includes bibliographical references at the end of each chapters and index.

Description based on print version record.

ISBN:

1-62948-659-0

OCLC:

918623804