دانلود کتاب Fractional Calculus in Analysis, Dynamics, and Optimal Control

فهرست مطالب :

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