Mathematical Techniques of Fractional Order Systems

Ahmad Taher Azar, Ahmed G. Radwan, Sundarapandian Vaidyanathan

• Publisher: Elsevier
• Year: 2018
• Print ISBN:
  9780128135921
• eBook ISBN:
  9780128135938
• Topic: Technology & Engineering
• Subtopic: Automation in Engineering
• Index: Technology & Engineering

Mathematical Techniques of Fractional Order Systems illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order circuit theorems from different perspectives in design, analysis and realizations, nonlinear fractional-order circuits and systems, the fractional-order memristive circuits and systems in design, analysis, emulators, simulation and experimental results. It is primarily meant for researchers from academia and industry, and for those working in areas such as control engineering, electrical engineering, computer science and information technology. This book is ideal for researchers working in the area of both continuous-time and discrete-time dynamics and chaotic systems. - Discusses multidisciplinary applications with new fundamentals, modeling, analysis, design, realization and experimental results - Includes circuits and systems based on new nonlinear elements - Covers most of the linear and nonlinear fractional-order theorems that will solve many scientific issues for researchers - Closes the gap between theoretical approaches and real-world applications - Provides MATLAB® and Simulink code for many applications in the book

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• List of Contributors
• Preface
• Chapter 1. Variable Order Fractional Derivatives and Bone Remodeling in the Presence of Metastases
• Chapter 2. Nonlinear Fractional Order Boundary-Value Problems With Multiple Solutions
• Chapter 3. Fractional Order System Forced-response Decomposition and Its Application
• Chapter 4. Exact Solution of Linear Fractional Distributed Order Systems With Exponential Order Weight Functions
• Chapter 5. Fractional Order Time-Varying-Delay Systems: A Delay-Dependent Stability Criterion by Using Diffusive Representation
• Chapter 6. Fractional Order Error Models With Parameter Constraints
• Chapter 7. Controllability of Single-valued and Multivalued Fractional Stochastic Differential Equations
• Chapter 8. Controllability of Fractional Higher Order Stochastic Integrodifferential Inclusions
• Chapter 9. Design of Fractional Order Fuzzy Sliding Mode Controller for Nonlinear Complex Systems
• Chapter 10. Sliding Mode Stabilization and Synchronization of Fractional Order Complex Chaotic and Hyperchaotic Systems
• Chapter 11. Multiswitching Synchronization of Commensurate Fractional Order Hyperchaotic Systems Via Active Control
• Chapter 12. Dual Combination Synchronization Scheme for Nonidentical Different Dimensional Fractional Order Systems Using Scaling Matrices
• Chapter 13. On the Fractional Order Generalized Discrete Maps
• Chapter 14. Applications of Continuous-time Fractional Order Chaotic Systems
• Chapter 15. Multiswitching Synchronization Between Chaotic Fractional Order Systems of Different Dimensions
• Chapter 16. Dynamics, Synchronization and Fractional Order Form of a Chaotic System With Infinite Equilibria
• Chapter 17. Chaotic Properties of Various Types of Hidden Attractors in Integer and Fractional Order Domains
• Chapter 18. Parameters Identification of Fractional Order Permanent Magnet Synchronous Motor Models Using Chaotic Meta-Heuristic Algorithms
• Chapter 19. Control and Synchronization of a Fractional Order Hyperchaotic System via Backstepping and Active Backstepping Approach
• Chapter 20. Enhanced Fractional Order Indirect Fuzzy Adaptive Synchronization of Uncertain Fractional Chaotic Systems Based on the Variable Structure Control: Robust H∞ Design Approach
• Chapter 21. On the Synchronization and Recurrence of Fractional Order Chaotic Systems
• Index