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...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Cresson, Jacky (Editor )
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York : Nova Publishers, [2014]
Colección:Mathematics research developments series.
Temas:
Fractional calculus.
Dérivées fractionnaires.
MATHEMATICS > Calculus.
MATHEMATICS > Mathematical Analysis.
Fractional calculus
Acceso en línea:Texto completo
Tabla de Contenidos:
  • ""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""

Ejemplares similares