Non Integer Order Calculus And Its Applications

Author : Piotr Ostalczyk,Dominik Sankowski,Jacek Nowakowski
Publisher : Springer
Page : 229 pages
File Size : 55,6 Mb
Release : 2018-03-22
Category : Technology & Engineering
ISBN : 9783319784588

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Non-Integer Order Calculus and its Applications by Piotr Ostalczyk,Dominik Sankowski,Jacek Nowakowski Pdf

This book focuses on fractional calculus, presenting novel advances in both the theory and applications of non-integer order systems. At the end of the twentieth century it was predicted that it would be the calculus of the twenty-first century, and that prophecy is confirmed year after year. Now this mathematical tool is successfully used in a variety of research areas, like engineering (e.g. electrical, mechanical, chemical), dynamical systems modeling, analysis and synthesis (e.g technical, biological, economical) as well as in multidisciplinary areas (e.g. biochemistry, electrochemistry).As well as the mathematical foundations the book concentrates on the technical applications of continuous-time and discrete-time fractional calculus, investigating the identification, analysis and control of electrical circuits and dynamical systems. It also presents the latest results.Although some scientific centers and scientists are skeptical and actively criticize the applicability of fractional calculus, it is worth breaking through the scientific and technological walls. Because the “fractional community” is growing rapidly there is a pressing need for the exchange of scientific results. The book includes papers presented at the 9th International Conference on Non-integer Order Calculus and Its Applications and is divided into three parts:• Mathematical foundations• Fractional systems analysis and synthesis• System modelingSeven papers discuss the mathematical foundations, twelve papers address fractional order analysis and synthesis and three focus on dynamical system modeling by the fractional order differential and difference equations. It is a useful resource for fractional calculus scientific community.

Author : Agnieszka B. Malinowska,Dorota Mozyrska,Łukasz Sajewski
Publisher : Springer
Page : 307 pages
File Size : 53,7 Mb
Release : 2019-04-17
Category : Technology & Engineering
ISBN : 9783030173449

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Advances in Non-Integer Order Calculus and Its Applications by Agnieszka B. Malinowska,Dorota Mozyrska,Łukasz Sajewski Pdf

This book provides an overview of some recent findings in the theory and applications of non-integer order systems. Discussing topics ranging from the mathematical foundations to technical applications of continuous-time and discrete-time fractional calculus, it includes 22 original research papers and is subdivided into four parts: • Mathematical Foundations • Approximation, Modeling and Simulations • Fractional Systems Analysis and Control • Applications The papers were selected from those presented at the 10th International Conference of Non-integer Order Calculus and its Applications, which was held at the Bialystok University of Technology, Poland, September 20–21, 2018. Thanks to the broad spectrum of topics covered, the book is suitable for researchers from applied mathematics and engineering. It is also a valuable resource for graduate students, as well as for scholars looking for new mathematical tools.

Author : Artur Babiarz,Adam Czornik,Jerzy Klamka,Michał Niezabitowski
Publisher : Springer
Page : 512 pages
File Size : 47,8 Mb
Release : 2016-09-15
Category : Technology & Engineering
ISBN : 9783319454740

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Theory and Applications of Non-integer Order Systems by Artur Babiarz,Adam Czornik,Jerzy Klamka,Michał Niezabitowski Pdf

This book collects papers from the 8th Conference on Non-Integer Order Calculus and Its Applications that have been held on September 20-21, 2016 in Zakopane, Poland. The preceding two conferences were held in Szczecin, Poland in 2015, and in Opole, Poland, in 2014. This conference provides a platform for academic exchange on the theory and application of fractional calculus between domestic and international universities, research institutes, corporate experts and scholars. The Proceedings of the 8th Conference on Non-Integer Order Calculus and Its Applications 2016 brings together rigorously reviewed contributions from leading international experts. The included papers cover novel various important aspects of mathematical foundations of fractional calculus, modeling and control of fractional systems as well as controllability, detectability, observability and stability problems for this systems.

Author : Wojciech Mitkowski,Janusz Kacprzyk,Jerzy Baranowski
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 55,5 Mb
Release : 2013-06-03
Category : Technology & Engineering
ISBN : 9783319009339

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Advances in the Theory and Applications of Non-integer Order Systems by Wojciech Mitkowski,Janusz Kacprzyk,Jerzy Baranowski Pdf

This volume presents various aspects of non-integer order systems, also known as fractional systems, which have recently attracted an increasing attention in the scientific community of systems science, applied mathematics, control theory. Non-integer systems have become relevant for many fields of science and technology exemplified by the modeling of signal transmission, electric noise, dielectric polarization, heat transfer, electrochemical reactions, thermal processes, acoustics, etc. The content is divided into six parts, every of which considers one of the currently relevant problems. In the first part the Realization problem is discussed, with a special focus on positive systems. The second part considers stability of certain classes of non-integer order systems with and without delays. The third part is focused on such important aspects as controllability, observability and optimization especially in discrete time. The fourth part is focused on distributed systems where non-integer calculus leads to new and interesting results. The next part considers problems of solutions and approximations of non-integer order equations and systems. The final and most extensive part is devoted to applications. Problems from mechatronics, biomedical engineering, robotics and others are all analyzed and solved with tools from fractional systems. This volume came to fruition thanks to high level of talks and interesting discussions at RRNR 2013 - 5th Conference on Non-integer Order Calculus and its Applications that took place at AGH University of Science and Technology in Kraków, Poland, which was organized by the Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering.

Author : Krzysztof J. Latawiec,Marian Łukaniszyn,Rafał Stanisławski
Publisher : Springer
Page : 296 pages
File Size : 54,9 Mb
Release : 2014-08-16
Category : Technology & Engineering
ISBN : 9783319099002

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Advances in Modelling and Control of Non-integer-Order Systems by Krzysztof J. Latawiec,Marian Łukaniszyn,Rafał Stanisławski Pdf

This volume presents selected aspects of non-integer, or fractional order systems, whose analysis, synthesis and applications have increasingly become a real challenge for various research communities, ranging from science to engineering. The spectrum of applications of the fractional order calculus has incredibly expanded, in fact it would be hard to find a science/engineering-related subject area where the fractional calculus had not been incorporated. The content of the fractional calculus is ranged from pure mathematics to engineering implementations and so is the content of this volume. The volume is subdivided into six parts, reflecting particular aspects of the fractional order calculus. The first part contains a single invited paper on a new formulation of fractional-order descriptor observers for fractional-order descriptor continous LTI systems. The second part provides new elements to the mathematical theory of fractional-order systems. In the third part of this volume, a bunch of new results in approximation, modeling and simulations of fractional-order systems is given. The fourth part presents new solutions to some problems in controllability and control of non-integer order systems, in particular fractional PID-like control. The fifth part analyzes the stability of non-integer order systems and some new results are offered in this important respect, in particular for discrete-time systems. The final, sixth part of this volume presents a spectrum of applications of the noninteger order calculus, ranging from bi-fractional filtering, in particular of electromyographic signals, through the thermal diffusion and advection diffusion processes to the SIEMENS platform implementation. This volume's papers were all subjected to stimulating comments and discussions from the active audience of the RRNR'2014, the 6th Conference on Non-integer Order Calculus and Its Applications that was organized by the Department of Electrical, Control and Computer Engineering, Opole University of Technology, Opole, Poland.

Author : Stefan Domek,Paweł Dworak
Publisher : Springer
Page : 293 pages
File Size : 47,8 Mb
Release : 2015-08-20
Category : Technology & Engineering
ISBN : 9783319230399

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Theoretical Developments and Applications of Non-Integer Order Systems by Stefan Domek,Paweł Dworak Pdf

This volume is devoted to presentation of new results of research on systems of non-integer order, called also fractional systems. Their analysis and practical implementation have been the object of spontaneous development for a few last decades. The fractional order models can depict a physical plant better than the classical integer order ones. This covers different research fields such as insulator properties, visco-elastic materials, electrodynamic, electrothermal, electrochemical, economic processes modelling etc. On the other hand fractional controllers often outperform their integer order counterparts. This volume contains new ideas and examples of implementation, theoretical and pure practical aspects of using a non-integer order calculus. It is divided into four parts covering: mathematical fundamentals, modeling and approximations, controllability, observability and stability problems and practical applications of fractional control systems. The first part expands the base of tools and methods of the mathematical basis for non-integer order calculus. Part two focuses on new methods and developments in process modeling and fractional derivatives approximations. In the third part a bunch of papers which raise problems of controllability, observability and stability of non-integer order systems is provided. Part four is devoted to presentation of different fractional order control applications. This book was created thanks to many experts in the field of fractional calculus: authors, anonymous referees whose comments allowed us to improve the final form of the papers and active and inspiring discussion of the participants of RRNR'2015, the 7th Conference on Non-Integer Order Calculus and Its Applications that was organized by the Faculty of Electrical Engineering, West Pomeranian University of Technology, Szczecin, Poland.

Author : J. Sabatier,O. P. Agrawal,J. A. Tenreiro Machado
Publisher : Springer Science & Business Media
Page : 550 pages
File Size : 50,6 Mb
Release : 2007-07-28
Category : Technology & Engineering
ISBN : 9781402060427

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Advances in Fractional Calculus by J. Sabatier,O. P. Agrawal,J. A. Tenreiro Machado Pdf

In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

Author : Roy Abi Zeid Daou,Xavier Moreau
Publisher : Nova Science Publishers
Page : 0 pages
File Size : 55,7 Mb
Release : 2014-01-11
Category : Fractional calculus
ISBN : 1634630025

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Fractional Calculus by Roy Abi Zeid Daou,Xavier Moreau Pdf

The first volume of this two-volume book, presents history, the mathematical modelling 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 initialisation of such systems is shown in chapter seven. In fact, this chapter presents a generalised application of the Hankel operator for initialisation 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.

Author : B. Ross
Publisher : Springer
Page : 391 pages
File Size : 43,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540699750

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Fractional Calculus and Its Applications by B. Ross Pdf

Author : Anonim
Publisher : Elsevier
Page : 322 pages
File Size : 49,9 Mb
Release : 1974-09-05
Category : Mathematics
ISBN : 0080956203

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The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order by Anonim Pdf

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Author : Piotr Kulczycki,Józef Korbicz,Janusz Kacprzyk
Publisher : Springer Nature
Page : 398 pages
File Size : 50,5 Mb
Release : 2022-01-04
Category : Technology & Engineering
ISBN : 9783030899721

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Fractional Dynamical Systems: Methods, Algorithms and Applications by Piotr Kulczycki,Józef Korbicz,Janusz Kacprzyk Pdf

This book presents a wide and comprehensive spectrum of issues and problems related to fractional-order dynamical systems. It is meant to be a full-fledge, comprehensive presentation of many aspects related to the broadly perceived fractional-order dynamical systems which constitute an extension of the traditional integer-order-type descriptions. This implies far-reaching consequences, both analytic and algorithmic, because—in general—properties of the traditional integer-order systems cannot be directly extended by a straightforward generalization to fractional-order systems, modeled by fractional-order differential equations involving derivatives of an non-integer order. This can be useful for describing and analyzing, for instance, anomalies in the behavior of various systems, chaotic behavior, etc. The book contains both analytic contributions with state-of-the-art and theoretical foundations, algorithmic implementation of tools and techniques, and—finally—some examples of relevant and successful practical applications.

Author : Anatoly Kochubei,Yuri Luchko
Publisher : Walter de Gruyter GmbH & Co KG
Page : 489 pages
File Size : 45,9 Mb
Release : 2019-02-19
Category : Mathematics
ISBN : 9783110571622

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Basic Theory by Anatoly Kochubei,Yuri Luchko Pdf

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.

Author : Devendra Kumar,Jagdev Singh
Publisher : CRC Press
Page : 153 pages
File Size : 49,7 Mb
Release : 2020-07-09
Category : Technology & Engineering
ISBN : 9781000081855

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Fractional Calculus in Medical and Health Science by Devendra Kumar,Jagdev Singh Pdf

This book covers applications of fractional calculus used for medical and health science. It offers a collection of research articles built into chapters on classical and modern dynamical systems formulated by fractional differential equations describing human diseases and how to control them. The mathematical results included in the book will be helpful to mathematicians and doctors by enabling them to explain real-life problems accurately. The book will also offer case studies of real-life situations with an emphasis on describing the mathematical results and showing how to apply the results to medical and health science, and at the same time highlighting modeling strategies. The book will be useful to graduate level students, educators and researchers interested in mathematics and medical science.

Author : Varsha Daftardar-Gejji
Publisher : ALPHA SCIENCE INTERNATIONAL LIMITED
Page : 232 pages
File Size : 51,6 Mb
Release : 2013-07-26
Category : Mathematics
ISBN : 9788184874785

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Fractional Calculus by Varsha Daftardar-Gejji Pdf

FRACTIONAL CALCULUS: Theory and Applications deals with differentiation and integration of arbitrary order. The origin of this subject can be traced back to the end of seventeenth century, the time when Newton and Leibniz developed foundations of differential and integral calculus. Nonetheless, utility and applicability of FC to various branches of science and engineering have been realized only in last few decades. Recent years have witnessed tremendous upsurge in research activities related to the applications of FC in modeling of real-world systems. Unlike the derivatives of integral order, the non-local nature of fractional derivatives correctly models many natural phenomena containing long memory and give more accurate description than their integer counterparts.The present book comprises of contributions from academicians and leading researchers and gives a panoramic overview of various aspects of this subject: Introduction to Fractional Calculus Fractional Differential Equations Fractional Ordered Dynamical Systems Fractional Operators on Fractals Local Fractional Derivatives Fractional Control Systems Fractional Operators and Statistical Distributions Applications to Engineering

Author : Piotr Kulczycki,Józef Korbicz,Janusz Kacprzyk
Publisher : Springer Nature
Page : 843 pages
File Size : 45,5 Mb
Release : 2020-09-03
Category : Technology & Engineering
ISBN : 9783030485870

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Automatic Control, Robotics, and Information Processing by Piotr Kulczycki,Józef Korbicz,Janusz Kacprzyk Pdf

This book presents a wide and comprehensive range of issues and problems in various fields of science and engineering, from both theoretical and applied perspectives. The desire to develop more effective and efficient tools and techniques for dealing with complex processes and systems has been a natural inspiration for the emergence of numerous fields of science and technology, in particular control and automation and, more recently, robotics. The contributions gathered here concern the development of methods and algorithms to determine best practices regarding broadly perceived decisions or controls. From an engineering standpoint, many of them focus on how to automate a specific process or complex system. From a tools-based perspective, several contributions address the development of analytic and algorithmic methods and techniques, devices and systems that make it possible to develop and subsequently implement the automation and robotization of crucial areas of human activity. All topics discussed are illustrated with sample applications.