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Fractional calculus : applications /
After presenting the first volume of this two-volume book, presenting a lot of mathematical and theoretical studies and research related to non-integer calculus, the second volume illustrates applications related to this domain. This volume is made up of 11 chapters. The first chapter presents the h...
| Clasificación: | Libro Electrónico |
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| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hauppauge, New York :
Nova Science Publishers, Inc.,
[2014]
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| Colección: | Mathematics research developments series.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- FRACTIONAL CALCULUS: APPLICATIONS; FRACTIONAL CALCULUS: APPLICATIONS; LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA; CONTENTS; FOREWORD; PREFACE; Chapter 1: THE HEURISTIC POWER OF THE NON INTEGERDIFFERENTIAL OPERATOR IN PHYSICS:FROM CHAOS TO EMERGENCE, AUTO-ORGANISATIONS AND HOLISTIC RULES; Abstract; 1. Introduction; 2. A Nice Equation for an Heuristic Power; 3. SWOT Method, Non Integer Diff-Integral and Co-Dimension; 4. The Generalization of the Exponential Concept; 5. Diffusion Under Field; 6. Riemann Zeta Function and Non-Integer Differentiation; 7. Auto Organization and Emergence.
- ConclusionAcknowledgment; References; Chapter 2: DYNAMICS OF FRACTIONAL ORDER CHAOTIC SYSTEMS; Abstract; 1. Introduction; 2. Preliminaries; 3. The Model; 4. Numerical Simulations; 5. Synchronization; 6. Conclusion; Acknowledgments; References; Chapter 3: PRESSURE CONTROL OF CNG ENGINESBY NON-INTEGER ORDER CONTROLLERS:A NEW TREND IN APPLICATION OF FRACTIONALCALCULUS TO AUTOMOTIVE SYSTEMS; Abstract; 1. Introduction: A Short Literature Review; 2. The Injection System; 3. The Control Strategy: Switching of Fractional Order Controllers by Gain Scheduling; 4. Fractional Order Control Design.
- 5. Simulation Results6. Conclusion; Acknowledgment; References; Chapter 4: LINEAR INTEGER ORDER SYSTEM CONTROL BY FRACTIONAL PI-STATE FEEDBACK; Abstract; Introduction; 1. Basic Definitions and Preliminaries; 2. Pole Placement Based Design of the Fractional Pi-State Feedback; 3. Bode's Ideal Transfer Function Based Design of FractionalPi-State Feedback; 5. Inverted Pendulum-Cart System Modeling and Swing-UpControl; 5. Implementation of the Fractional PI-State Feedbackto Stabilize the Inverted Pendulum-Cart System; Conclusion; Acknowledgments; References.
- Chapter 5: FROM THE FORMAL CONCEPT ANALYSISTO THE NUMERICAL SIMULATION OF THE THERMALDIFFUSION PHENOMENA IN A FINITE MEDIUMAbstract; 1. Context and Problematic; 2. Parameters and Definitions; 3. Semi-Infinite Plane; 4. Responses in the Semi-Infinite Plane; 5. Finite Plane; 6. Responses in Finite Plane; 7. Simulink Responses; Conclusion; References; Chapter 6: TEMPERATURE CONTROL OF A DIFFUSIVE MEDIUMUSING THE CRONE APPROACH; Abstract; 1. Introduction; 2. Modelling; 3. Temperature Control; 4. Conclusion; References.
- Chapter 7: ADAPTIVE SECOND-ORDER FRACTIONALSLIDING MODE CONTROL WITH APPLICATIONTO WATER TANKS LEVEL CONTROLAbstract; 1. Introduction; 2. Preliminaries; 3. Second Order Sliding Mode Control Strategy; 4. Adaptation Law Synthesis; 5. Numerical Studies; Conclusion; References; Chapter 8: FEATURES OF FRACTIONAL OPERATORSINVOLVING FRACTIONAL DERIVATIVESAND THEIR APPLICATIONS TO THE PROBLEMSOF MECHANICS OF SOLIDS; Abstract; 1. Introduction; 2. Rabotnov's Fractional Operators and Main Formulas of Algebra of Fractional Operators; 3. Generalized Rabotnov OperatorsGeneralized.