Fractional calculus : applications / Roy Abi Zeid Daou and Xavier Moreau, editors.

Format:

Book

Contributor:

Abi Zeid Daou, Roy, editor.

Moreau, Xavier, 1966- editor.

Series:

Mathematics research developments series.

Mathematics Research Developments

Language:

English

Subjects (All):

Fractional calculus.

Calculus.

Physical Description:

1 online resource (306 p.)

Place of Publication:

New York, [New York] : Nova Science Publishers, Inc., 2015.

Language Note:

English

Summary:

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 heuristic power of the non-integer differential operators in physics starting from the chaos to the emergence, the auto-organizations and the holistic rules. The second chapter shows the dynamics of the fractional order chaotic systems along with some applications. The third chapter represents the pr

Contents:

""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""; ""Conclusion""; ""Acknowledgment""; ""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 Results""; ""6. 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 MEDIUM""; ""Abstract""; ""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 CONTROL""; ""Abstract""; ""1. Introduction""; ""2. Preliminaries""; ""3. Second Order Sliding Mode Control Strategy""; ""4. Adaptation Law Synthesis""; ""5. Numerical Studies""

""Conclusion""

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:

1-63463-233-8

OCLC:

903957212