Fractional-Order Design

List of contributors

1. MOS realizations of fractional-order elements
Stavroula Kapoulea, Panagiotis Bertsias, Costas Psychalinos, and Ahmed S. Elwakil

1.1. Introduction

1.2. CPE/FI emulation techniques

1.3. Practical aspects

1.4. Conclusions and discussion
Acknowledgment
References

2. A chaotic system with equilibria located on a line and its fractional-order form
Karthikeyan Rajagopal, Fahimeh Nazarimehr, Alireza Bahramian, and Sajad Jafari

2.1. Introduction

2.2. Model of the proposed flow and its dynamics

2.3. Fractional-order form

2.4. Circuit implementation

2.5. FPGA implementation of the chaotic system

2.6. Conclusion
References

3. Approximation of fractional-order elements for sinusoidal oscillators
Shalabh K. Mishra, Dharmendra K. Upadhyay, and Maneesha Gupta

3.1. Introduction

3.2. R-C network-based FDs

3.3. FDs for sinusoidal oscillators

3.4. Performance analysis

3.5. Conclusion and scope of future research
References

4. Synchronization between fractional chaotic maps with different dimensions
Adel Ouannas, Amina-Aicha Khennaoui, Iqbal M. Batiha, and Viet-Thanh Pham

4.1. Introduction

4.2. Preliminaries

4.3. Combined synchronization of 2D fractional maps

4.4. Combined synchronization of 3D fractional maps

4.5. Concluding remarks and future works
Acknowledgments
References

5. Stabilization of different dimensional fractional chaotic maps
Adel Ouannas, Amina-Aicha Khennaoui, Iqbal M. Batiha, and Viet-Thanh Pham

5.1. Introduction

5.2. Basic tools

5.3. Stabilization of 2D fractional maps

5.4. Stabilization of 3D fractional maps

5.5. Summary and future works
Acknowledgments
References

6. Observability of speed DC motor with self-tuning fuzzy-fractional-order controller
Arezki Fekik, Mohamed Lamine Hamida, Hamza Houassine, Hakim Denoun, Sundarapandian Vaidyanathan, Nacera Yassa, Ahmed G. Radwan, and Lobna A. Said

6.1. Introduction

6.2. Mathematical model of DC motor

6.3. Stability of speed estimation

6.4. Proposed speed controller

6.5. Results and discussion

6.6. Conclusions
References

7. Chaos control and fractional inverse matrix projective difference synchronization on parallel chaotic systems with application
Pushali Trikha, Lone Seth Jahanzaib, and Ayub Khan

7.1. Introduction

7.2. Preliminaries

7.3. The fractional inverse matrix projective difference synchronization

7.4. Illustration in secure communication

7.5. Conclusions
References

8. Aggregation of chaotic signal with proportional fractional derivative execution in communication and circuit simulation
Najeeb Alam Khan, Saeed Akbar, Muhammad Ali Qureshi, and Tooba Hameed

8.1. Introduction

8.2. Fractional-order chaotic systems and their properties

8.3. Analog circuit imitation

8.4. Security analysis

8.5. Conclusion
References

9. CNT-based fractors in all four quadrants: design, simulation, and practical applications
Avishek Adhikary

9.1. Introduction

9.2. Fractor: definitions and state-of-the-art

9.3. A wide-CPZ, long-life, packaged CNT fractor

9.4. Fractors with desired specifications

9.5. Four-quadrant FO immittances using CNT fractors

9.6. Application of four-quadrant CNT fractors

9.7. Conclusion
Appendix 9.A MATLAB program to determine RC ladder parameters for five FO specifications
Acknowledgments
References

10. Fractional-order systems in biological applications: estimating causal relations in a system with inner connectivity using fractional moments
Zahra Tabanfar, Farnaz Ghassemi, Alireza Bahramian, Ali Nouri, Ensieh Ghaffari Shad, and Sajad Jafari

10.1. Introduction

10.2. Related work

10.3. Fractional moments and fractional cumulants

10.4. Hindmarsh–Rose model

10.5. Estimating causal relations

10.6. Causal direction pattern recognition

10.7. Discussion

10.8. Conclusion
References

11. Unitary fractional-order derivative operators for quantum computation
Baris Baykant Alagoz and Serkan Alagoz

11.1. Introduction

11.2. A brief survey on geometric phase concepts in quantum computation

11.3. Methodology

11.4. Some quantum computation implications for unitary fractional-order derivative operators

11.5. Discussion and conclusions
Appendix 11.A
References

12. Analysis and realization of fractional step filters of order (1 + α)
Gagandeep Kaur, A.Q. Ansari, and M.S. Hashmi

12.1. Introduction

12.2. Analysis of fractional step filters

12.3. Numerical analysis and simulations of FSFs of order (1 + α)

12.4. Stability

12.5. Sensitivity analysis

12.6. Conclusion
References

13. Fractional-order identification and synthesis of equivalent circuit for electrochemical system based on pulse voltammetry
Sanjeev Kumar and Arunangshu Ghosh

13.1. Introduction

13.2. Experimental setup

13.3. Fractional-order models

13.4. Identification of fractional-order transfer function

13.5. Proposed circuit with fractional-order elements

13.6. Principal component analysis: towards electronic tongue application

13.7. Conclusions
References

14. Higher-order fractional elements: realizations and applications
Neeta Pandey, Rajeshwari Pandey, and Rakesh Verma

14.1. Introduction

14.2. Realization of FOEs with fractional order < 1

14.3. Realization of fractional-order element with 1 < fractional order < n

14.4. Application

14.5. Conclusion
References

15. Fabrication of polymer nanocomposite-based fractional-order capacitor: a guide
Zaid Mohammad Shah, Farooq Ahmad Khanday, Gul Faroz Ahmad Malik, and Zahoor Ahmad Jhat

15.1. Introduction

15.2. Polymers

15.3. Ferroelectric polymers

15.4. Conductive fillers

15.5. Methods of synthesis

15.6. Percolation threshold

15.7. Factors affecting properties of polymer NCs

15.8. A GNS/PVDF FOC

15.9. Conclusion
Acknowledgments
References

16. Design guidelines for fabrication of MWCNT-polymer based solid-state fractional capacitor
Dina Anna John and Karabi Biswas

16.1. Introduction

16.2. Solid-state fractional capacitors

16.3. Batch analysis of the solid-state fractional capacitors for defining the guidelines

16.4. Validation of the defined guidelines

16.5. Material characterization

16.6. Correlating the material characterization with the CPA of a solid-state fractional capacitor

16.7. Conclusion
Acknowledgments
References

Index