Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation

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Springer Science & Business Media, May 30, 2011 - Technology & Engineering - 218 pages
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"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order.

The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level.

Ivo Petráš is an Associate Professor of automatic control and the Director of the Institute of Control and Informatization of Production Processes, Faculty of BERG, Technical University of Košice, Slovak Republic. His main research interests include control systems, industrial automation, and applied mathematics.

 

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Contents

Chapter 1 Introduction
1
Chapter 2 Fractional Calculus
6
Chapter 3 FractionalOrder Systems
43
Chapter 4 Stability of FractionalOrder Systems
55
Chapter 5 FractionalOrder Chaotic Systems
103
Chapter 6 Control of FractionalOrder Chaotic Systems
185
Chapter 7 Conclusion
200
Appendix A A List of Matlab Functions
207
Appendix B Laplace and Inverse Laplace Transforms
210
Glossary
215
Index
217
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