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Author: Bruce J. West Publisher: CRC Press ISBN: 1040012698 Category : Mathematics Languages : en Pages : 147
Book Description
This book is the first of its kind on fractional calculus (FC), dedicated to advocating for FC in STEM education and research. Fractional calculus is increasingly used today, but there remains a core population of skeptics regarding the utility of this "new" calculus. This book is intended for those who are skeptical about the need for fractional calculus to describe dynamic complex networks and must be convinced of its use on a case-by-case basis. It is a one-stop resource to rapidly read and replace the appropriate skepticism with new knowledge. It offers compelling reasons from the perspectives of the physical, social, and life sciences as to why fractional calculus is needed when addressing the complexity of an underlying STEM phenomenon. The six chapters are accompanied by useful and essential appendices and chapter-end references. Each includes new (fractional-order) ways of thinking about statistics, complexity dynamics, and what constitutes a solution to a complexity science problem. The book will appeal to students and researchers in all STEM-related fields, such as engineering, physics, biology and biomedicine, climate change, big data, and machine learning. It is also suitable for general readers interested in these fields.
Author: Bruce J. West Publisher: CRC Press ISBN: 1040012698 Category : Mathematics Languages : en Pages : 147
Book Description
This book is the first of its kind on fractional calculus (FC), dedicated to advocating for FC in STEM education and research. Fractional calculus is increasingly used today, but there remains a core population of skeptics regarding the utility of this "new" calculus. This book is intended for those who are skeptical about the need for fractional calculus to describe dynamic complex networks and must be convinced of its use on a case-by-case basis. It is a one-stop resource to rapidly read and replace the appropriate skepticism with new knowledge. It offers compelling reasons from the perspectives of the physical, social, and life sciences as to why fractional calculus is needed when addressing the complexity of an underlying STEM phenomenon. The six chapters are accompanied by useful and essential appendices and chapter-end references. Each includes new (fractional-order) ways of thinking about statistics, complexity dynamics, and what constitutes a solution to a complexity science problem. The book will appeal to students and researchers in all STEM-related fields, such as engineering, physics, biology and biomedicine, climate change, big data, and machine learning. It is also suitable for general readers interested in these fields.
Author: Bruce J. West Publisher: ISBN: 9781003468561 Category : Mathematics Languages : en Pages : 0
Book Description
"This book is the first of its kind on fractional calculus (FC), dedicated to advocating for FC in STEM education and research. Fractional calculus is increasingly used today, but there remains a core population of skeptics regarding the utility of this "new" calculus. This book is intended for those who are skeptical about the need for fractional calculus to describe dynamic complex networks and must be convinced of its use on a case-by-case basis. It is a one-stop resource to rapidly read and replace the appropriate skepticism with new knowledge. It offers compelling reasons from the perspectives of the physical, social, and life sciences as to why fractional calculus is needed when addressing the complexity of an underlying STEM phenomenon. The six chapters are accompanied by useful and essential appendices and chapter-end references. Each includes new (fractional-order) ways of thinking about statistics, complexity dynamics, and what constitutes a solution to a complexity science problem. The book will appeal to students and researchers in all STEM-related fields, engineering, physics, biology and biomedicine, climate change, big data, machine learning, etc. It is also suitable for general readers interested in these fields"--
Author: Bruce J. West Publisher: CRC Press ISBN: 1040089135 Category : Mathematics Languages : en Pages : 162
Book Description
On the Fractal Language of Medicine bridges a very clear gap among the knowledge gained over the last 20 years in the physical and life sciences on network theory, organ synchronicity and communication, the understanding of fractal signatures in health and disease and the importance of fractional calculus in integrating these concepts. The authors opine that the field of medicine has not appreciated this hard-won knowledge and has suffered greatly as a result. This book addresses this perceived deficiency by introducing medical researchers, clinicians, residents, first-year medical students and members of allied fields to the work of the so-called hard sciences. It seeks to facilitate effective communication between empiricists and theorists by making interdisciplinary efforts to explain complex mathematical concepts to physicians and, equally important, to elucidate complex medical concepts to physicists or mathematicians. This book will be of great interest to medical students, professionals and academics, as well as students and researchers of applied mathematics, especially those interested in fractional calculus and fractals.
Author: J. Sabatier Publisher: Springer Science & Business Media ISBN: 1402060424 Category : Technology & Engineering Languages : en Pages : 550
Book Description
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: Hu Sheng Publisher: Springer Science & Business Media ISBN: 144712233X Category : Technology & Engineering Languages : en Pages : 310
Book Description
Fractional processes are widely found in science, technology and engineering systems. In Fractional Processes and Fractional-order Signal Processing, some complex random signals, characterized by the presence of a heavy-tailed distribution or non-negligible dependence between distant observations (local and long memory), are introduced and examined from the ‘fractional’ perspective using simulation, fractional-order modeling and filtering and realization of fractional-order systems. These fractional-order signal processing (FOSP) techniques are based on fractional calculus, the fractional Fourier transform and fractional lower-order moments. Fractional Processes and Fractional-order Signal Processing: presents fractional processes of fixed, variable and distributed order studied as the output of fractional-order differential systems; introduces FOSP techniques and the fractional signals and fractional systems point of view; details real-world-application examples of FOSP techniques to demonstrate their utility; and provides important background material on Mittag–Leffler functions, the use of numerical inverse Laplace transform algorithms and supporting MATLAB® codes together with a helpful survey of relevant webpages. Readers will be able to use the techniques presented to re-examine their signals and signal-processing methods. This text offers an extended toolbox for complex signals from diverse fields in science and engineering. It will give academic researchers and practitioners a novel insight into the complex random signals characterized by fractional properties, and some powerful tools to analyze those signals.
Author: Bruce J. West Publisher: CRC Press ISBN: 149873801X Category : Mathematics Languages : en Pages : 303
Book Description
This book is not a text devoted to a pedagogical presentation of a specialized topic nor is it a monograph focused on the author's area of research. It accomplishes both these things while providing a rationale for why the reader ought to be interested in learning about fractional calculus. This book is for researchers who has heard about many
Author: Snehashish Chakraverty Publisher: Elsevier ISBN: 0443154058 Category : Mathematics Languages : en Pages : 288
Book Description
Computation and Modeling for Fractional Order Systems provides readers with problem-solving techniques for obtaining exact and/or approximate solutions of governing equations arising in fractional dynamical systems presented using various analytical, semi-analytical, and numerical methods. In this regard, this book brings together contemporary and computationally efficient methods for investigating real-world fractional order systems in one volume. Fractional calculus has gained increasing popularity and relevance over the last few decades, due to its well-established applications in various fields of science and engineering. It deals with the differential and integral operators with non-integral powers. Fractional differential equations are the pillar of various systems occurring in a wide range of science and engineering disciplines, namely physics, chemical engineering, mathematical biology, financial mathematics, structural mechanics, control theory, circuit analysis, and biomechanics, among others. The fractional derivative has also been used in various other physical problems, such as frequency-dependent damping behavior of structures, motion of a plate in a Newtonian fluid, PID controller for the control of dynamical systems, and many others. The mathematical models in electromagnetics, rheology, viscoelasticity, electrochemistry, control theory, Brownian motion, signal and image processing, fluid dynamics, financial mathematics, and material science are well defined by fractional-order differential equations. Generally, these physical models are demonstrated either by ordinary or partial differential equations. However, modeling these problems by fractional differential equations, on the other hand, can make the physics of the systems more feasible and practical in some cases. In order to know the behavior of these systems, we need to study the solutions of the governing fractional models. The exact solution of fractional differential equations may not always be possible using known classical methods. Generally, the physical models occurring in nature comprise complex phenomena, and it is sometimes challenging to obtain the solution (both analytical and numerical) of nonlinear differential equations of fractional order. Various aspects of mathematical modeling that may include deterministic or uncertain (viz. fuzzy or interval or stochastic) scenarios along with fractional order (singular/non-singular kernels) are important to understand the dynamical systems. Computation and Modeling for Fractional Order Systems covers various types of fractional order models in deterministic and non-deterministic scenarios. Various analytical/semi-analytical/numerical methods are applied for solving real-life fractional order problems. The comprehensive descriptions of different recently developed fractional singular, non-singular, fractal-fractional, and discrete fractional operators, along with computationally efficient methods, are included for the reader to understand how these may be applied to real-world systems, and a wide variety of dynamical systems such as deterministic, stochastic, continuous, and discrete are addressed by the authors of the book.
Author: Bruce J. West Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110534274 Category : Mathematics Languages : en Pages : 244
Book Description
Complexity increases with increasing system size in everything from organisms to organizations. The nonlinear dependence of a system’s functionality on its size, by means of an allometry relation, is argued to be a consequence of their joint dependency on complexity (information). In turn, complexity is proven to be the source of allometry and to provide a new kind of force entailed by a system‘s information gradient. Based on first principles, the scaling behavior of the probability density function is determined by the exact solution to a set of fractional differential equations. The resulting lowest order moments in system size and functionality gives rise to the empirical allometry relations. Taking examples from various topics in nature, the book is of interest to researchers in applied mathematics, as well as, investigators in the natural, social, physical and life sciences. Contents Complexity Empirical allometry Statistics, scaling and simulation Allometry theories Strange kinetics Fractional probability calculus
Author: Boulkroune, Abdesselem Publisher: IGI Global ISBN: 152255419X Category : Computers Languages : en Pages : 562
Book Description
In the recent years, fractional-order systems have been studied by many researchers in the engineering field. It was found that many systems can be described more accurately by fractional differential equations than by integer-order models. Advanced Synchronization Control and Bifurcation of Chaotic Fractional-Order Systems is a scholarly publication that explores new developments related to novel chaotic fractional-order systems, control schemes, and their applications. Featuring coverage on a wide range of topics including chaos synchronization, nonlinear control, and cryptography, this publication is geared toward engineers, IT professionals, researchers, and upper-level graduate students seeking current research on chaotic fractional-order systems and their applications in engineering and computer science.
Author: Indranil Pan Publisher: Springer ISBN: 3642315496 Category : Technology & Engineering Languages : en Pages : 305
Book Description
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.
Author: Bruce J. West
Author: Bruce J. West
Author: Bruce J. West
Author: Bruce J. West
Author: J. Sabatier
Author: Hu Sheng
Author: Bruce J. West
Author: Snehashish Chakraverty
Author: Bruce J. West
Author: Boulkroune, Abdesselem
Author: Indranil Pan