Fractional Order Systems
An Overview of Mathematics, Design, and Applications for Engineers
- 1st Edition - October 13, 2021
- Imprint: Academic Press
- Editors: Ahmed G. Radwan, Farooq Ahmad Khanday, Lobna A. Said
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 8 2 4 2 9 3 - 3
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 2 4 3 3 4 - 3
Fractional Order Systems: An Overview of Mathematics, Design, and Applications for Engineers introduces applications from a design perspective, helping readers plan and design th… Read more
Purchase options
Institutional subscription on ScienceDirect
Request a sales quoteFractional Order Systems: An Overview of Mathematics, Design, and Applications for Engineers introduces applications from a design perspective, helping readers plan and design their own applications. The book includes the different techniques employed to design fractional-order systems/devices comprehensively and straightforwardly. Furthermore, mathematics is available in the literature on how to solve fractional-order calculus for system applications. This book introduces the mathematics that has been employed explicitly for fractional-order systems. It will prove an excellent material for students and scholars who want to quickly understand the field of fractional-order systems and contribute to its different domains and applications.
Fractional-order systems are believed to play an essential role in our day-to-day activities. Therefore, several researchers around the globe endeavor to work in the different domains of fractional-order systems. The efforts include developing the mathematics to solve fractional-order calculus/systems and to achieve the feasible designs for various applications of fractional-order systems.
- 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 possible new applications for 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. Researchers from biological sciences to understand the theories better therein
- Cover image
- Title page
- Table of Contents
- Copyright
- List of contributors
- Chapter One: A survey on numerical studies for fractional biological models and their optimal control
- Abstract
- 1.1. Introduction
- 1.2. Primary definitions of fractional calculus
- 1.3. Fractional optimal control problem
- 1.4. A survey on fractional biological models and their optimal control
- 1.5. A survey on numerical methods for solving fractional optimal control biological models
- 1.6. A novel fractional-order malaria mathematical model
- 1.7. HFOCP
- 1.8. Numerical experiment and discussion
- 1.9. Conclusions
- References
- Chapter Two: A collection of interdisciplinary applications of fractional-order circuits
- Abstract
- Acknowledgements
- 2.1. Introduction
- 2.2. Implementation of the approximated Laplacian operator
- 2.3. Biomedical signal processing applications
- 2.4. Bio-impedance applications
- 2.5. Sensor applications
- 2.6. Conclusions and discussion
- References
- Chapter Three: Fractional-order control
- Abstract
- Acknowledgement
- 3.1. Introduction
- 3.2. Fractional-order systems and controllers
- 3.3. New fractional-order control techniques
- 3.4. Discussion and conclusions
- References
- Chapter Four: Fractional-order systems, numerical techniques, and applications
- Abstract
- 4.1. Introduction
- 4.2. Numerical methods for solving the multiterm time-fractional diffusion-wave equation
- 4.3. Analytical solution of the multiterm time-fractional differential equation and application to unsteady flow of generalized viscoelastic fluid
- 4.4. Numerical analysis of multiterm time-fractional viscoelastic non-Newtonian fluid models for simulating unsteady MHD Couette flow of generalized Oldroyd-B fluid
- 4.5. A fractional alternating-direction implicit method for a multiterm time-space fractional Bloch–Torrey equation in 3D
- References
- Chapter Five: Fractional-order systems, numerical techniques, and applications
- Abstract
- 5.1. Introduction
- 5.2. Unstructured-mesh Galerkin finite element method for the 2D multiterm time-space fractional Bloch–Torrey equations on irregular convex domains
- 5.3. Finite difference/finite element method for a 2D multiterm time-fractional mixed subdiffusion and diffusion-wave equation on convex domains
- 5.4. Alternating-direction implicit spectral Galerkin method for the multiterm time-space fractional diffusion equation in three dimensions
- 5.5. Space-time spectral method for the multiterm time-fractional diffusion equations
- References
- Chapter Six: Chaos in fractional-order difference systems
- Abstract
- Acknowledgement
- 6.1. Introduction
- 6.2. Basic concepts
- 6.3. Chaos in 2D fractional difference systems
- 6.4. Chaos in 3D fractional difference system
- 6.5. Concluding remarks and future works
- References
- Chapter Seven: A review on the realization of fractional-order devices to use as sensors and circuit elements for experimental studies and research
- Abstract
- 7.1. Introduction
- 7.2. A brief history of the development of fractional-order elements (FOEs)
- 7.3. Research work on single-component FOEs
- 7.4. Research work on multicomponent FOEs
- 7.5. Application of FOE as a sensor
- 7.6. Applications of FOE in circuits and systems
- 7.7. Conclusion
- References
- Chapter Eight: FPAA-based implementation of fractional-order multidirectional multiscroll chaotic oscillators
- Abstract
- 8.1. Introduction
- 8.2. Multidirectional and multiscroll chaotic oscillator
- 8.3. Multidirectional and multiscroll FOCO
- 8.4. Implementation of a multidirectional and multiscroll FOCO by FPAA
- 8.5. Conclusion
- References
- Chapter Nine: A survey on memristor active emulation circuits in the fractional-order domain
- Abstract
- Acknowledgement
- 9.1. Introduction
- 9.2. Memristive theory
- 9.3. Memristor application
- 9.4. Different memristance emulation circuits
- 9.5. PSPICE simulations and experimental results
- 9.6. Conclusion
- References
- Chapter Ten: Fractional-order oscillators based on a single Op-Amp
- Abstract
- Acknowledgement
- 10.1. Introduction
- 10.2. Fractional-order oscillators
- 10.3. Family of single-Op-Amp oscillators with two fractional-order capacitors
- 10.4. PSPICE simulation and experimental results
- 10.5. Conclusion
- References
- Chapter Eleven: Fractional calculus in electronic circuits: a review
- Abstract
- 11.1. Introduction
- 11.2. Fractional-order circuit elements or fractors
- 11.3. Fractional-order RLC circuits
- 11.4. Design of fractional-order filters
- 11.5. Fractional-order oscillators
- 11.6. Recent trends in FO circuit synthesis
- 11.7. Conclusion and discussion
- References
- Chapter Twelve: Dynamics and implementation techniques of fractional-order neuron models: a survey
- Abstract
- 12.1. Introduction
- 12.2. Neuron models
- 12.3. Literature survey
- 12.4. General dynamical analysis of fractional-order model
- 12.5. Dynamical investigation of the Hindmarsh–Rose neuron model
- 12.6. Implementation techniques of fractional-order neuron models
- 12.7. Conclusion
- References
- Chapter Thirteen: Fractional calculus: applications in rheology
- Abstract
- 13.1. Introduction
- 13.2. Fractional calculus and transforms
- 13.3. Rheology, basic concepts
- 13.4. Fractional calculus in rheology for viscoelastic materials
- 13.5. Some rheological fractional anti-Zener models with Weyl fractional derivative
- 13.6. The (α,β)-Burgers model with Caputo derivative
- 13.7. Conclusion
- References
- Chapter Fourteen: Introduction of new kernels and new models to solve the drawbacks of fractional integration/differentiation operators and classical fractional-order models
- Abstract
- 14.1. Introduction
- 14.2. Fractional-order models and associated drawbacks
- 14.3. Some new kernels
- 14.4. Volterra equations
- 14.5. Other alternative models to capture power-law type behaviors
- 14.6. Conclusion
- Appendix 14.A.
- References
- Index
- Edition: 1
- Published: October 13, 2021
- Imprint: Academic Press
- No. of pages: 612
- Language: English
- Paperback ISBN: 9780128242933
- eBook ISBN: 9780128243343
AR
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, EgyptFK
Farooq Ahmad 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
University of Kashmir, Srinagar, IndiaLS
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), EgyptRead Fractional Order Systems on ScienceDirect