Fractional-Order Design

Fractional-Order Design

Devices, Circuits, and Systems

1st Edition - October 22, 2021

Write a review

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

Purchase options

Purchase options
DRM-free (PDF, EPub)
Sales tax will be calculated at check-out

Institutional Subscription

Free Global Shipping
No minimum order


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


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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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

    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


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.

Affiliations and Expertise

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

Ratings and Reviews

Write a review

There are currently no reviews for "Fractional-Order Design"