# Fractional-Order Design

### Devices, Circuits, and Systems

1st Edition - October 22, 2021

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• Editors: Ahmed G. Radwan, Farooq Ahmed Khanday, Lobna A. Said
• Paperback ISBN: 9780323900904
• eBook ISBN: 9780323902045

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## Description

Fractional-Order Design: Devices, Circuits, and Systems introduces applications from the design perspective so that the reader can learn about, and get ready to, design these applications. The book also includes the different techniques employed to comprehensively and straightforwardly design fractional-order systems/devices. Furthermore, a lot of mathematics is available in the literature for solving the fractional-order calculus for system application. However, a small portion is employed in the design of fractional-order systems. This book introduces the mathematics that has been employed explicitly for fractional-order systems. Students and scholars who wants to quickly understand the field of fractional-order systems and contribute to its different domains and applications will find this book a welcomed resource.

## Key Features

• Presents a simple and comprehensive understanding of the field of fractional-order systems
• Offers practical knowledge on the design of fractional-order systems for different applications
• Exposes users to the possible new areas of applications of fractional-order systems

## Readership

Researchers, graduate students in the fields of basic and applied sciences, electrical engineering, chemical engineering, information security, control theory, solid-state electronics, power engineering, biomedical engineering

## Table of Contents

• 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

## Product details

• No. of pages: 548
• Language: English
• Copyright: © Academic Press 2021
• Published: October 22, 2021
• Imprint: Academic Press
• Paperback ISBN: 9780323900904
• eBook ISBN: 9780323902045

## About the Editors

### Ahmed G. Radwan

Ahmed G. Radwan (Senior member IEEE) is a Professor in the Engineering Mathematics Department, Cairo University, Egypt, and Acting Director of Research, Nile University, Egypt. He was the Former Director of Nanoelectronics Integrated Systems Center (NISC), Nile University, Egypt. Dr. Radwan was a visiting Professor in Computational Electromagnetic Lab (CEL), Electrical and Computer Engineering department (ECE), McMaster University, Canada in the interval [2008 – 2009], then he was selected to be a part of the first foundation research teams to join KAUST (King Abdullah University of Science and Technology) during the interval [2009 -2011]. His research interests include interdisciplinary concepts between mathematics and engineering applications such as fractional-order systems, bifurcation, chaos, memristor, and encryption. Dr. Radwan received the Cairo University excellence award for research in the engineering sciences in 2016, the Abdul Hameed Shoman Award for Arab Researchers in basic sciences in 2015, the state achievements award for research in mathematical sciences in 2012, the Cairo University achievements award for research in the engineering sciences in 2013, and the best researcher awards Nile University 2015 & 2016. Dr. Radwan has more than 200 papers, h-index 30, and more than 3000 citations based on Scopus database. He is the Co-inventor of Six US patents, author/Co-author of Seven international books as well as 15-chapter books in the highly ranked publishers such as Elsevier and Springer. He received many research grants as Principle Investigator (PI), CO-PI, or Consultant from different national/international organizations. He was Invited to be Lead/Guest Editors in Journal of Circuits, Systems and Signal Processing, and Journal of Mathematical Problems in Engineering, and Complexity. He organized many special sessions, serve as TPC (Technical Program Committee) in several international conferences. He was selected as a member of the first scientific council of Egyptian Young Academy of Sciences (EYAS) as well as in the first scientific council of the Egyptian Center for the Advancement of Science, Technology, and Innovation (ECASTI) to empower and encourage Egyptian young scientists in science and technology and build knowledge-based societies.

#### Affiliations and Expertise

IEEE Senior Member, Professor, Engineering, Mathematics and Physics Department, Faculty of Engineering, Cairo University; Nanoelectronics Integrated Systems Center (NISC), Nile University, Cairo, Egypt

### Farooq Ahmed Khanday

Farooq Ahmad Khanday (M’15, SM’19) received B.Sc., M.Sc., M. Phil. and Ph.D. Degrees from the University of Kashmir in 2001, 2004 2010 and 2013 respectively. From June 2005 to Jan. 2009, he served as Assistant Professor on a contractual basis at the University of Kashmir, Department of Electronics and Instrumentation Technology. In 2009, Dr. Khanday joined the Department of Higher Education J&K and Department of Electronics and Vocational Studies, Islamia College of Science and Commerce Srinagar, as Assistant Professor. In May 2010, he joined as Assistant Professor in the Department of Electronics and Instrumentation Technology, University of Kashmir. His research interests include Fractional-order Circuits, Nano-Electronics, Low-voltage analog integrated circuit design, Hardware Neural Network, Quantum Computing, Stochastic Computing, and Biomedical Circuit Design. Dr. Khanday is the author or co-author of more than 85 publications in peer-reviewed indexed International and National journals/conferences of repute and three book chapters. A book of Dr. Khanday on “Nanoscale Electronic Devices and their Applications” is to appear in July 2020. Dr. Khanday is the Management Committee (MC) Observer of the COST Action CA15225 (Fractional-order systems - analysis, synthesis, and their importance for future design) of the European Union. He is the senior member of IEEE and a member of several professional societies. Dr. Khanday is serving as a reviewer for many reputed International and National scientific journals in Electronics. He has successfully guided many Ph.D., M. Phil scholars, and M. Tech thesis. Dr. Khanday also has completed/ongoing funded research projects to his credit and has established laboratories with state of the art facilities for pursuing research in the field of IC design, Nanoelectronics, fractional-order systems, etc.

Srinagar India

### Lobna A. Said

Lobna A. Said is a full-time Assistant Professor at the Faculty of Engineering and Applied Science and the Nano-Electronics Integrated System Research Center (NISC), Nile University (NU). She received the B.Sc. , the M.Sc., and the Ph.D. degrees in electronics and communications from Cairo University, Egypt, in 2007, 2011, and 2016, respectively. She has H-index 15, and more than 660 citations based on the Scopus database. She has over 85 publications distributed between high-impact journals, conferences, and book chapters. She was involved in many research grants as a Senior Researcher, or as a Co-PI from different national organizations. Her research interests are interdisciplinary, including system modeling, control techniques, optimization techniques, analog and digital integrated circuits, fractional-order circuits and systems, non-linear analysis, and chaos theory. She has received the Recognized Reviewer Award from many international journals. She is the Vice-Chair of research activities at the IEEE Computational Intelligence Egypt Chapter. She has received the Excellence Award from the Center for the Development of Higher education and Research in 2016. She is the Winner of Dr. Hazem Ezzat Prize for the outstanding researcher, NU 2019. She is one of the top 10 researchers at NU for the year 2018-2019. Recently, she was selected as a member of the Egyptian Young Academy of Sciences (EYAS) to empower and encourage young Egyptian scientists in science and technology and build knowledge-based societies. In 2020, she was selected to be an affiliate member of the African Academy of Science (AAS). She is in the technical program committee for many International Conferences.

#### Affiliations and Expertise

Assistant Professor, Faculty of Engineering and Applied Science, Nano-Electronics Integrated System Research Center (NISC), Nile University (NU), Egypt

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