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The design and realization of continuous- time fractional order circuits and their performance analysis have been presented. Here, a fractional order devices which is primarily used for realization of fractional order circuits, are described. Also a comparison between the fractional order circuits and its integer order counterpart has been presented. It can be shown by simulation that the fractional order circuits can be used for high frequency application without changing RC time constant of the circuits. This helps to design a high speed analog circuits as compared to classical integer order circuits.
Two half-order differentiator circuit designs were investigated and their electrical performance evaluated (Oldham and Oldfield). Initially, each circuit design was computer modelled and simulated using the HSPICE computer analysis program. Then, each circuit design (Oldham and Oldfield) was fabricated with two different component technologies. This resulted in four circuits, realized on printed circuit boards, to be evaluated--Oldham discrete component; Oldham hybrid component; Oldfield discrete component; and Oldfield surface mount component. The characterizations of each circuit's electrical performance is documented with time, phase, gain, noise and spectrum responses. A comparison of each circuit's performance versus the design criteria and computer model performance is presented. Based upon the comparison of the circuit's electrical performances, the circuits were rank ordered as follows: 1. Oldham integrated chip technology (hybrid) component circuit design; 2. Oldham discrete component circuit design; 3. Oldfield surface mount component circuit design; 4. Oldfield discrete component design. Electrical Circuits, Fractional Calculus, Very Large Scale Integration, Printed Circuit Boards, Half-Order Differentiation.
A guide to the new research in the field of fractional order analysis Fractional Order Analysis contains the most recent research findings in fractional order analysis and its applications. The authors—noted experts on the topic—offer an examination of the theory, methods, applications, and the modern tools and techniques in the field of fractional order analysis. The information, tools, and applications presented can help develop mathematical methods and models with better accuracy. Comprehensive in scope, the book covers a range of topics including: new fractional operators, fractional derivatives, fractional differential equations, inequalities for different fractional derivatives and fractional integrals, fractional modeling related to transmission of Malaria, and dynamics of Zika virus with various fractional derivatives, and more. Designed to be an accessible text, several useful, relevant and connected topics can be found in one place, which is crucial for an understanding of the research problems of an applied nature. This book: Contains recent development in fractional calculus Offers a balance of theory, methods, and applications Puts the focus on fractional analysis and its interdisciplinary applications, such as fractional models for biological models Helps make research more relevant to real-life applications Written for researchers, professionals and practitioners, Fractional Order Analysis offers a comprehensive resource to fractional analysis and its many applications as well as information on the newest research.
This book describes a new type of passive electronic components, called fractal elements, from a theoretical and practical point of view. The authors discuss in detail the physical implementation and design of fractal devices for application in fractional-order signal processing and systems. The concepts of fractals and fractal signals are explained, as well as the fundamentals of fractional calculus. Several implementations of fractional impedances are discussed, along with comparison of their performance characteristics. Details of design, schematics, fundamental techniques and implementation of RC-based fractal elements are provided.
Fractional 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
This book details the simulation and optimization of integer and fractional-order chaotic systems, and how they can be implemented in the analog and digital domains using FPAAs and FPGAs. Design guidelines are provided to use commercially available electronic devices, and to perform hardware descriptions of integer/fractional-order chaotic systems programming in VHDL. Finally, several engineering applications oriented to cryptography, internet of things, robotics and chaotic communications, are detailed to highlight the usefulness of FPAA/FPGA based integer/fractional-order chaotic systems. Provides guidelines to implement fractional-order derivatives using commercially available devices; Describes details on using FPAAs to approach fractional-order chaotic systems; Includes details on using FPGAs to approach fractional-order chaotic systems, programming in VHDL and reducing hardware resources; Discusses applications to cryptography, internet of things, robotics and chaotic communications.
This monograph covers some selected problems of positive and fractional electrical circuits composed of resistors, coils, capacitors and voltage (current) sources. The book consists of 8 chapters, 4 appendices and a list of references. Chapter 1 is devoted to fractional standard and positive continuous-time and discrete-time linear systems without and with delays. In chapter 2 the standard and positive fractional electrical circuits are considered and the fractional electrical circuits in transient states are analyzed. Descriptor linear electrical circuits and their properties are investigated in chapter 3, while chapter 4 is devoted to the stability of fractional standard and positive linear electrical circuits. The reachability, observability and reconstructability of fractional positive electrical circuits and their decoupling zeros are analyzed in chapter 5. The fractional linear electrical circuits with feedbacks are considered in chapter 6. In chapter 7 solutions of minimum energy control for standard and fractional systems with and without bounded inputs is presented. In chapter 8 the fractional continuous-time 2D linear systems described by the Roesser type models are investigated.
This book focuses on two specific areas related to fractional order systems – the realization of physical devices characterized by non-integer order impedance, usually called fractional-order elements (FOEs); and the characterization of vegetable tissues via electrical impedance spectroscopy (EIS) – and provides readers with new tools for designing new types of integrated circuits. The majority of the book addresses FOEs. The interest in these topics is related to the need to produce “analogue” electronic devices characterized by non-integer order impedance, and to the characterization of natural phenomena, which are systems with memory or aftereffects and for which the fractional-order calculus tool is the ideal choice for analysis. FOEs represent the building blocks for designing and realizing analogue integrated electronic circuits, which the authors believe hold the potential for a wealth of mass-market applications. The freedom to choose either an integer- or non-integer-order analogue integrator/derivator is a new one for electronic circuit designers. The book shows how specific non-integer-order impedance elements can be created using materials with specific structural properties. EIS measures the electrical impedance of a specimen across a given range of frequencies, producing a spectrum that represents the variation of the impedance versus frequency – a technique that has the advantage of avoiding aggressive examinations. Biological tissues are complex systems characterized by dynamic processes that occur at different lengths and time scales; this book proposes a model for vegetable tissues that describes the behavior of such materials by considering the interactions among various relaxing phenomena and memory effects.
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. 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