Mathematical Techniques of Fractional Order Systems

Mathematical Techniques of Fractional Order Systems

1st Edition - June 11, 2018

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  • Editors: Ahmad Taher Azar, Ahmed Radwan, Sundarapandian Vaidyanathan
  • eBook ISBN: 9780128135938
  • Paperback ISBN: 9780128135921

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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.

Key Features

  • 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


Researchers from academia and industry, who are working in the research areas of control engineering, electrical engineering, computer science, and information technology

Table of Contents

  • 1. Analog and digital realization of nonlinear fractional order systems
    2. Bifurcation analysis and control
    3. Chaos analysis, control and anti-control
    4. Chaos modeling and control applications
    5. Control and synchronization of complex networks
    6. Discrete chaotic maps and their applications
    7. Fractional order modelling of physical systems
    8. Fractional system identification and optimization
    9. Fuzzy fractional order controller
    10. Nonlinear circuit analysis and applications
    11. Random number generators and encryption in integer and fractional order domains
    12. Recent nontechnology applications based on memristors, memcapacitors, and meminductor elements

Product details

  • No. of pages: 700
  • Language: English
  • Copyright: © Elsevier 2018
  • Published: June 11, 2018
  • Imprint: Elsevier
  • eBook ISBN: 9780128135938
  • Paperback ISBN: 9780128135921

About the Editors

Ahmad Taher Azar

Prof. Ahmad Azar has received the M.Sc. degree in 2006 and Ph.D degree in 2009 from Faculty of Engineering, Cairo University, Egypt. He is a research associate Professor at Prince Sultan University, Riyadh, Kingdom Saudi Arabia. He is also an associate professor at the Faculty of Computers and Artificial intelligence, Benha University, Egypt. Prof. Azar is the Editor in Chief of International Journal of System Dynamics Applications (IJSDA) and International Journal of Service Science, Management, Engineering, and Technology (IJSSMET) published by IGI Global, USA. Also, he is the Editor in Chief of International Journal of Intelligent Engineering Informatics (IJIEI), Inderscience Publishers, Olney, UK. Prof. Azar has worked as associate editor of IEEE Trans. Neural Networks and Learning Systems from 2013 to 2017. He is currently Associate Editor of ISA Transactios, Elsevier and IEEE systems journal. Dr. Ahmad Azar has worked in the areas of Control Theory & Applications, Process Control, Chaos Control and Synchronization, Nonlinear control, Renewable Energy, Computational Intelligence and has authored/coauthored over 200 research publications in peer-reviewed reputed journals, book chapters and conference proceedings. He is an editor of many books in the field of fuzzy logic systems, modeling techniques, control systems, computational intelligence, chaos modeling and machine learning. Dr. Ahmad Azar is closely associated with several international journals as a reviewer. He serves as international programme committee member in many international and peer-reviewed conferences. Dr. Ahmad Azar has been a senior member of IEEE since December 2013 due to his significant contributions to the profession. Dr. Ahmad Azar is the recipient of several awards including: Benha University Prize for Scientific Excellence (2015, 2016, 2017 and 2018), the paper citation award from Benha University (2015, 2016, 2017 and 2018). In June 2018, Prof. Azar was awarded the Egyptian State Prize in Engineering Sciences, the Academy of Scientific Research and Technology of Egypt, 2017. In July 2018 he was selected as a member of Energy and Electricity Research council, Academy of Scientific Research, Ministry of Higher Education. In August 2018 he was selected as senior member of International Rough Set Society (IRSS).

Affiliations and Expertise

Research Associate Professor, Prince Sultan University, Riyadh, Kingdom Saudi Arabia; Associate Professor, Faculty of Computers and Artificial intelligence, Benha University, Egypt

Ahmed 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

Sundarapandian Vaidyanathan

=Sundarapandian Vaidyanathan received his Doctor of Science degree in Electrical and Systems Engineering from Washington University in St. Louis, USA in 1996. He is currently professor at the Research and Development Centre, Vel Tech University at Avadi, Chennai, Tamil Nadu, India. Previously, he was a Professor and Acting Director at the Indian Institute of Information Technology and Management-Kerala, Trivandrum, India. Prof. Vaidyanathan’s main research interests are Control Systems, Dynamical Systems, Chaos Theory, Intelligent Control, Systems Modelling and Computational Science. He has over 25 years of teaching and research experience. He has published over 475 research papers indexed by Scopus. He has published many text-books and edited research monographs for reputed publishers. Prof. Vaidyanathan is the Editor-in-Chief of International Journal of Nonlinear Dynamics and Control (IJNDC), Inderscience, Olney, UK. He is an Associate Editor of International Journal of Intelligent Engineering Informatics (IJIEI), Inderscience, Olney, UK. He is also an Associate Editor of International Journal of Automation and Control (IJAAC), Inderscience, Olney, UK. Prof. Vaidyanathan has guest-edited many Special Issues for Inderscience and Hindawi journals. Prof. Vaidyanathan is in the Editorial Boards of many reputed international journals. In the SciVal-Scopus World Rankings based on Field-Weighted Citation Impact (FWCI), Prof. Vaidyanathan is ranked #19 in Computer Science and #1 in Mathematics for the 5-years period (2014-2018). In March 2018, Careers-360 (India) conferred the Best Research Faculty Award in Computer Science in India to Prof. Vaidyanathan for the academic year 2017-2018 and he received this prestigious research award from Mr. Prakash Javadekar, Honourable Union Minister for Human Resource Development in India. Prof. Vaidyanathan has delivered plenary lectures on Control Systems, Scientific Computing and Chaos Theory in many international conferences. He has conducted several workshops on MATLAB and SCILAB in India and abroad.

Affiliations and Expertise

Professor, Research and Development Centre, Vel Tech University, Avadi, Chennai-600 062, Tamil Nadu, India

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