Mathematical Techniques Of Fractional Order Systems

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Mathematical Techniques of Fractional Order Systems

Mathematical Techniques of Fractional Order Systems
  • Author : Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan
  • Publisher : Elsevier
  • Release Date : 2018-06-11
  • Total pages : 700
  • ISBN : 9780128135938
  • File Size : 47,7 Mb
  • Total Download : 873
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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. 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

Fractional Order Systems

Fractional Order Systems
  • Author : Ahmed G. Radwan,Farooq Ahmad Khanday,Lobna A. Said
  • Publisher : Academic Press
  • Release Date : 2021-10-13
  • Total pages : 612
  • ISBN : 9780128243343
  • File Size : 37,5 Mb
  • Total Download : 195
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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

Mathematical Techniques of Fractional Order Systems

Mathematical Techniques of Fractional Order Systems
  • Author : Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan
  • Publisher : Unknown
  • Release Date : 2018-06
  • Total pages : 500
  • ISBN : 0128135921
  • File Size : 16,7 Mb
  • Total Download : 297
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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. 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(R) and Simulink code for many applications in the book

Fractional Order Systems

Fractional Order Systems
  • Author : Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan
  • Publisher : Academic Press
  • Release Date : 2018-08-16
  • Total pages : 741
  • ISBN : 9780128163085
  • File Size : 37,5 Mb
  • Total Download : 999
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Fractional Order Systems: Optimization, Control, Circuit Realizations and Applications consists of 21 contributed chapters by subject experts. Chapters offer practical solutions and novel methods for recent research problems in the multidisciplinary applications of fractional order systems, such as FPGA, circuits, memristors, control algorithms, photovoltaic systems, robot manipulators, oscillators, etc. This book is ideal for researchers working in the modeling and applications of both continuous-time and discrete-time dynamics and chaotic systems. Researchers from academia and industry who are working in research areas such as control engineering, electrical engineering, mechanical engineering, computer science, and information technology will find the book most informative. Discusses multi-disciplinary applications with new fundamentals, modeling, analysis, design, realization and experimental results Includes new circuits and systems based on the 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 of the applications in the book

Fractional Order Systems and Applications in Engineering

Fractional Order Systems and Applications in Engineering
  • Author : Dumitru Baleanu,Valentina Emilia Balas,Praveen Agarwal
  • Publisher : Academic Press
  • Release Date : 2022-12-01
  • Total pages : 392
  • ISBN : 9780323909549
  • File Size : 27,6 Mb
  • Total Download : 966
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Fractional Order Systems and Applications in Engineering presents the use of fractional calculus (calculus of non-integer order) in the description and modelling of systems and in a range of control design and practical applications. The book covers the fundamentals of fractional calculus together with some analytical and numerical techniques, and provides MATLAB® codes for the simulation of fractional-order control (FOC) systems. The use of fractional calculus can improve and generalize well-established control methods and strategies. Many different FOC schemes are presented for control and dynamic systems problems. These extend to the challenging control engineering design problems of robust and nonlinear control. Practical material relating to a wide variety of applications including, among others, mechatronics, civil engineering, irrigation and water management, and biological systems is also provided. All the control schemes and applications are presented with either system simulation results or real experimental results, or both. Fractional Order Systems and Applications in Engineering introduces readers to the essentials of FOC and imbues them with a basic understanding of FOC concepts and methods. With this knowledge readers can extend their use of FOC in other industrial system applications, thereby expanding their range of disciplines by exploiting this versatile new set of control techniques. Provides the most recent and up-to-date developments on the Fractional-order Systems and their analyzing process Integrates recent advancements of modeling of real phenomena (on Fractional-order Systems) via different-different mathematical equations with demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering Provides readers with illustrative examples of how to use the presented theories of Fractional-order Systems in specific cases with associated MATLAB code

Fractional Order Processes

Fractional Order Processes
  • Author : Seshu Kumar Damarla,Madhusree Kundu
  • Publisher : CRC Press
  • Release Date : 2018-09-03
  • Total pages : 211
  • ISBN : 9780429996887
  • File Size : 54,5 Mb
  • Total Download : 413
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The book presents efficient numerical methods for simulation and analysis of physical processes exhibiting fractional order (FO) dynamics. The book introduces FO system identification method to estimate parameters of a mathematical model under consideration from experimental or simulated data. A simple tuning technique, which aims to produce a robust FO PID controller exhibiting iso-damping property during re-parameterization of a plant, is devised in the book. A new numerical method to find an equivalent finite dimensional integer order system for an infinite dimensional FO system is developed in the book. The book also introduces a numerical method to solve FO optimal control problems. Key features Proposes generalized triangular function operational matrices. Shows significant applications of triangular orthogonal functions as well as triangular strip operational matrices in simulation, identification and control of fractional order processes. Provides numerical methods for simulation of physical problems involving different types of weakly singular integral equations, Abel’s integral equation, fractional order integro-differential equations, fractional order differential and differential-algebraic equations, and fractional order partial differential equations. Suggests alternative way to do numerical computation of fractional order signals and systems and control. Provides source codes developed in MATLAB for each chapter, allowing the interested reader to take advantage of these codes for broadening and enhancing the scope of the book itself and developing new results.

Methods of Mathematical Modelling

Methods of Mathematical Modelling
  • Author : Harendra Singh,Devendra Kumar,Dumitru Baleanu
  • Publisher : CRC Press
  • Release Date : 2019-09-17
  • Total pages : 238
  • ISBN : 9781000596786
  • File Size : 45,8 Mb
  • Total Download : 936
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This book features original research articles on the topic of mathematical modelling and fractional differential equations. The contributions, written by leading researchers in the field, consist of chapters on classical and modern dynamical systems modelled by fractional differential equations in physics, engineering, signal processing, fluid mechanics, and bioengineering, manufacturing, systems engineering, and project management. The book offers theory and practical applications for the solutions of real-life problems and will be of interest to graduate level students, educators, researchers, and scientists interested in mathematical modelling and its diverse applications. Features Presents several recent developments in the theory and applications of fractional calculus Includes chapters on different analytical and numerical methods dedicated to several mathematical equations Develops methods for the mathematical models which are governed by fractional differential equations Provides methods for models in physics, engineering, signal processing, fluid mechanics, and bioengineering Discusses real-world problems, theory, and applications

Backstepping Control of Nonlinear Dynamical Systems

Backstepping Control of Nonlinear Dynamical Systems
  • Author : Sundarapandian Vaidyanathan,Ahmad Taher Azar
  • Publisher : Academic Press
  • Release Date : 2020-08-15
  • Total pages : 532
  • ISBN : 9780128175835
  • File Size : 31,7 Mb
  • Total Download : 288
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Backstepping Control of Nonlinear Dynamical Systems addresses both the fundamentals of backstepping control and advances in the field. The latest techniques explored include ‘active backstepping control’, ‘adaptive backstepping control’, ‘fuzzy backstepping control’ and ‘adaptive fuzzy backstepping control’. The reference book provides numerous simulations using MATLAB and circuit design. These illustrate the main results of theory and applications of backstepping control of nonlinear control systems. Backstepping control encompasses varied aspects of mechanical engineering and has many different applications within the field. For example, the book covers aspects related to robot manipulators, aircraft flight control systems, power systems, mechanical systems, biological systems and chaotic systems. This multifaceted view of subject areas means that this useful reference resource will be ideal for a large cross section of the mechanical engineering community. Details the real-world applications of backstepping control Gives an up-to-date insight into the theory, uses and application of backstepping control Bridges the gaps for different fields of engineering, including mechanical engineering, aeronautical engineering, electrical engineering, communications engineering, robotics and biomedical instrumentation

Modeling and Control of Static Converters for Hybrid Storage Systems

Modeling and Control of Static Converters for Hybrid Storage Systems
  • Author : Fekik, Arezki,Benamrouche, Nacereddine
  • Publisher : IGI Global
  • Release Date : 2021-09-17
  • Total pages : 355
  • ISBN : 9781799874492
  • File Size : 31,9 Mb
  • Total Download : 153
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The energy transition initiated in recent years has enabled the growing integration of renewable production into the energy mix. Microgrids make it possible to maximize the efficiency of energy transmission from source to consumer by bringing the latter together geographically and by reducing losses linked to transport. However, the lack of inertia and the micro-grid support system makes it weak, and energy storage is necessary to ensure its proper functioning. Current storage technologies do not make it possible to provide both a large capacity of energy and power at the same time. Hybrid storage is a solution that combines the advantages of several technologies and reduces their disadvantages. Modeling and Control of Static Converters for Hybrid Storage Systems covers the modeling, control theorems, and optimization techniques that solve many scientific problems for researchers in the field of power converter control for renewable energy hybrid storage and places particular emphasis on the modeling and control of static converters for hybrid storage systems. Covering topics ranging from energy storage to power generation, this book is ideal for automation engineers, electrical engineers, mechanical engineers, professionals, scientists, academicians, master's and doctoral students, and researchers in the disciplines of electrical and mechanical engineering.

Fractional Order Systems

Fractional Order Systems
  • Author : Riccardo Caponetto
  • Publisher : World Scientific
  • Release Date : 2010
  • Total pages : 201
  • ISBN : 9789814304191
  • File Size : 39,8 Mb
  • Total Download : 720
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This book aims to propose implementations and applications of Fractional Order Systems (FOS). It is well known that FOS can be applied in control applications and systems modeling, and their effectiveness has been proven in many theoretical works and simulation routines. A further and mandatory step for FOS real world utilization is their hardware implementation and applications on real systems modeling. With this viewpoint, introductive chapters on FOS are included, on the definition of stability region of Fractional Order PID Controller and Chaotic FOS, followed by the practical implementation based on Microcontroller, Field Programmable Gate Array, Field Programmable Analog Array and Switched Capacitor. Another section is dedicated to FO modeling of Ionic Polymeric Metal Composite (IPMC). This new material may have applications in robotics, aerospace and biomedicine.

Fractional-Order Modeling of Dynamic Systems with Applications in Optimization, Signal Processing, and Control

Fractional-Order Modeling of Dynamic Systems with Applications in Optimization, Signal Processing, and Control
  • Author : Ahmed G. Radwan,Farooq Ahmad Khanday,Lobna A. Said
  • Publisher : Academic Press
  • Release Date : 2021-10-29
  • Total pages : 528
  • ISBN : 9780323902038
  • File Size : 22,9 Mb
  • Total Download : 239
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Fractional-order Modelling of Dynamic Systems with Applications in Optimization, Signal Processing and Control 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

Fractional Order Systems

Fractional Order Systems
  • Author : Anonim
  • Publisher : Unknown
  • Release Date : 2023
  • Total pages : 229
  • ISBN : 9789814465151
  • File Size : 37,6 Mb
  • Total Download : 531
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PDF book entitled Fractional Order Systems written by Anonim and published by Unknown which was released on 2023 with total hardcover pages 229, the book become popular and critical acclaim.

Intelligent Fractional Order Systems and Control

Intelligent Fractional Order Systems and Control
  • Author : Indranil Pan,Saptarshi Das
  • Publisher : Springer
  • Release Date : 2012-08-23
  • Total pages : 298
  • ISBN : 9783642315497
  • File Size : 28,9 Mb
  • Total Download : 646
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Fractional order calculus is finding increasing interest in the control system community. Hardware realizations of fractional order controllers have sparked off a renewed zeal into the investigations of control system design in the light of fractional calculus. As such many notions of integer order LTI systems are being modified and extended to incorporate these new concepts. Computational Intelligence (CI) techniques have been applied to engineering problems to find solutions to many hitherto intractable conundrums and is a useful tool for dealing with problems of higher computational complexity. This book borders on the interface between CI techniques and fractional calculus, and looks at ways in which fractional order control systems may be designed or enhanced using CI based paradigms. To the best of the author’s knowledge this is the first book of its kind exclusively dedicated to the application of computational intelligence techniques in fractional order systems and control. The book tries to assimilate various existing concepts in this nascent field of fractional order intelligent control and is aimed at researchers and post graduate students working in this field.

Advanced Applications of Fractional Differential Operators to Science and Technology

Advanced Applications of Fractional Differential Operators to Science and Technology
  • Author : Matouk, Ahmed Ezzat
  • Publisher : IGI Global
  • Release Date : 2020-04-24
  • Total pages : 401
  • ISBN : 9781799831242
  • File Size : 21,5 Mb
  • Total Download : 652
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Fractional-order calculus dates to the 19th century but has been resurrected as a prevalent research subject due to its provision of more adequate and realistic descriptions of physical aspects within the science and engineering fields. What was once a classical form of mathematics is currently being reintroduced as a new modeling technique that engineers and scientists are finding modern uses for. There is a need for research on all facets of these fractional-order systems and studies of its potential applications. Advanced Applications of Fractional Differential Operators to Science and Technology provides emerging research exploring the theoretical and practical aspects of novel fractional modeling and related dynamical behaviors as well as its applications within the fields of physical sciences and engineering. Featuring coverage on a broad range of topics such as chaotic dynamics, ecological models, and bifurcation control, this book is ideally designed for engineering professionals, mathematicians, physicists, analysts, researchers, educators, and students seeking current research on fractional calculus and other applied mathematical modeling techniques.

Proceedings of the International Conference on Advanced Intelligent Systems and Informatics 2020

Proceedings of the International Conference on Advanced Intelligent Systems and Informatics 2020
  • Author : Aboul Ella Hassanien,Adam Slowik,Václav Snášel,Hisham El-Deeb,Fahmy M. Tolba
  • Publisher : Springer Nature
  • Release Date : 2020-09-19
  • Total pages : 893
  • ISBN : 9783030586690
  • File Size : 22,5 Mb
  • Total Download : 514
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This book presents the proceedings of the 6th International Conference on Advanced Intelligent Systems and Informatics 2020 (AISI2020), which took place in Cairo, Egypt, from October 19 to 21, 2020. This international and interdisciplinary conference, which highlighted essential research and developments in the fields of informatics and intelligent systems, was organized by the Scientific Research Group in Egypt (SRGE). The book is divided into several sections, covering the following topics: Intelligent Systems, Deep Learning Technology, Document and Sentiment Analysis, Blockchain and Cyber Physical System, Health Informatics and AI against COVID-19, Data Mining, Power and Control Systems, Business Intelligence, Social Media and Digital Transformation, Robotic, Control Design, and Smart Systems.

Special Functions and Analysis of Differential Equations

Special Functions and Analysis of Differential Equations
  • Author : Praveen Agarwal,Ravi P Agarwal,Michael Ruzhansky
  • Publisher : CRC Press
  • Release Date : 2020-09-08
  • Total pages : 349
  • ISBN : 9781000078589
  • File Size : 19,9 Mb
  • Total Download : 811
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Differential Equations are very important tools in Mathematical Analysis. They are widely found in mathematics itself and in its applications to statistics, computing, electrical circuit analysis, dynamical systems, economics, biology, and so on. Recently there has been an increasing interest in and widely-extended use of differential equations and systems of fractional order (that is, of arbitrary order) as better models of phenomena in various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature, and so on. Now, new unified presentation and extensive development of special functions associated with fractional calculus are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations. This book provides learners with the opportunity to develop an understanding of advancements of special functions and the skills needed to apply advanced mathematical techniques to solve complex differential equations and Partial Differential Equations (PDEs). Subject matters should be strongly related to special functions involving mathematical analysis and its numerous applications. The main objective of this book is to highlight the importance of fundamental results and techniques of the theory of complex analysis for differential equations and PDEs and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Specific topics include but are not limited to Partial differential equations Least squares on first-order system Sequence and series in functional analysis Special functions related to fractional (non-integer) order control systems and equations Various special functions related to generalized fractional calculus Operational method in fractional calculus Functional analysis and operator theory Mathematical physics Applications of numerical analysis and applied mathematics Computational mathematics Mathematical modeling This book provides the recent developments in special functions and differential equations and publishes high-quality, peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential equations, and related applications.

Fractional Order Control and Synchronization of Chaotic Systems

Fractional Order Control and Synchronization of Chaotic Systems
  • Author : Ahmad Taher Azar,Sundarapandian Vaidyanathan,Adel Ouannas
  • Publisher : Springer
  • Release Date : 2017-02-27
  • Total pages : 877
  • ISBN : 9783319502496
  • File Size : 30,8 Mb
  • Total Download : 714
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The book reports on the latest advances in and applications of fractional order control and synchronization of chaotic systems, explaining the concepts involved in a clear, matter-of-fact style. It consists of 30 original contributions written by eminent scientists and active researchers in the field that address theories, methods and applications in a number of research areas related to fractional order control and synchronization of chaotic systems, such as: fractional chaotic systems, hyperchaotic systems, complex systems, fractional order discrete chaotic systems, chaos control, chaos synchronization, jerk circuits, fractional chaotic systems with hidden attractors, neural network, fuzzy logic controllers, behavioral modeling, robust and adaptive control, sliding mode control, different types of synchronization, circuit realization of chaotic systems, etc. In addition to providing readers extensive information on chaos fundamentals, fractional calculus, fractional differential equations, fractional control and stability, the book also discusses key applications of fractional order chaotic systems, as well as multidisciplinary solutions developed via control modeling. As such, it offers the perfect reference guide for graduate students, researchers and practitioners in the areas of fractional order control systems and fractional order chaotic systems.

Fractional Calculus: New Applications in Understanding Nonlinear Phenomena

Fractional Calculus: New Applications in Understanding Nonlinear Phenomena
  • Author : Mehmet Yavuz,Necati Özdemir
  • Publisher : Bentham Science Publishers
  • Release Date : 2022-12-14
  • Total pages : 275
  • ISBN : 9789815051940
  • File Size : 23,8 Mb
  • Total Download : 880
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In the last two decades, many new fractional operators have appeared, often defined using integrals with special functions in the kernel as well as their extended or multivariable forms. Modern operators in fractional calculus have different properties which are comparable to those of classical operators.These have been intensively studied formodelling and analysing real-world phenomena. There is now a growing body of research on new methods to understand natural occurrences and tackle different problems. This book presents ten reviews of recent fractional operators split over three sections: 1. Chaotic Systems and Control (covers the Caputo fractional derivative, and a chaotic fractional-order financial system)2. Heat Conduction (covers the Duhamel theorem for time-dependent source terms, and the Cattaneo–Hristov model for oscillatory heat transfer)3. Computational Methods and Their Illustrative Applications (covers mathematical analysis for understanding 5 real-word phenomena: HTLV-1 infection of CD4+ T-cells, traveling waves, rumor-spreading, biochemical reactions, and the computational fluid dynamics of a non-powered floating object navigating in an approach channel) This volume is a resource for researchers in physics, biology, behavioral sciences, and mathematics who are interested in new applications of fractional calculus in the study of nonlinear phenomena.

Mathematical Methods in Engineering and Applied Sciences

Mathematical Methods in Engineering and Applied Sciences
  • Author : Hemen Dutta
  • Publisher : CRC Press
  • Release Date : 2020-01-03
  • Total pages : 294
  • ISBN : 9781000764796
  • File Size : 40,9 Mb
  • Total Download : 218
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This book covers tools and techniques used for developing mathematical methods and modelling related to real-life situations. It brings forward significant aspects of mathematical research by using different mathematical methods such as analytical, computational, and numerical with relevance or applications in engineering and applied sciences. Presents theory, methods, and applications in a balanced manner Includes the basic developments with full details Contains the most recent advances and offers enough references for further study Written in a self-contained style and provides proof of necessary results Offers research problems to help early career researchers prepare research proposals Mathematical Methods in Engineering and Applied Sciences makes available for the audience, several relevant topics in one place necessary for crucial understanding of research problems of an applied nature. This should attract the attention of general readers, mathematicians, and engineers interested in new tools and techniques required for developing more accurate mathematical methods and modelling corresponding to real-life situations.

Fractional Calculus

Fractional Calculus
  • Author : Roy Abi Zeid Daou,Xavier Moreau
  • Publisher : Nova Science Pub Incorporated
  • Release Date : 2014-11-15
  • Total pages : 222
  • ISBN : 1634630025
  • File Size : 51,6 Mb
  • Total Download : 694
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The first volume of this two-volume book, presents history, the mathematical modeling and the applications of fractional order systems, and contains mathematical and theoretical studies and research related to this domain. This volume is made up of 11 chapters. The first chapter presents an analysis of the Caputo derivative and the pseudo state representation with the infinite state approach. The second chapter studies the stability of a class of fractional Cauchy problems. The third chapter shows how to solve fractional order differential equations and fractional order partial differential equations using modern matrix algebraic approaches. Following this chapter, chapter four proposes another analytical method to solve differential equations with local fractional derivative operators. Concerning chapter five, it presents the extended Borel transform and its related fractional analysis. After presenting the analytical resolution methods for fractional calculus, chapter six shows the essentials of fractional calculus on discrete settings. The initialization of such systems is shown in chapter seven. In fact, this chapter presents a generalized application of the Hankel operator for initialization of fractional order systems. The last four chapters show some new studies and applications of non-integer calculus. In fact, chapter eight presents the fractional reaction-transport equations and evanescent continuous time random walks. Chapter nine shows a novel approach in the exponential integrators for fractional differential equations. Chapter ten presents the non-fragile tuning of fractional order PD controllers for integrating time delay systems. At the end, chapter eleven proposes a discrete finite-dimensional approximation of linear infinite dimensional systems. To sum up, this volume presents a mathematical and theoretical study of fractional calculus along with a stability study and some applications. This volume ends up with some new techniques and methods applied in fractional calculus. This volume will be followed up by a second volume that focuses on the applications of fractional calculus in several engineering domains.

Fractional-Order Design

Fractional-Order Design
  • Author : Ahmed G. Radwan,Farooq Ahmad Khanday,Lobna A. Said
  • Publisher : Academic Press
  • Release Date : 2021-10-22
  • Total pages : 548
  • ISBN : 9780323902045
  • File Size : 36,7 Mb
  • Total Download : 423
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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