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Fractional Calculus for Skeptics I

The Fractal Paradigm

$This book is the first of its kind on fractional calculus (FC), dedicated to advocating for FC in STEM education and research. Fractional calculus is increasingly used today, but there remains a core population of skeptics regarding the utility of this "new" calculus. This book is intended for those who are skeptical about the need for fractional calculus to describe dynamic complex networks and must be convinced of its use on a case-by-case basis. It is a one-stop resource to rapidly read and replace the appropriate skepticism with new knowledge. It offers compelling reasons from the perspectives of the physical, social, and life sciences as to why fractional calculus is needed when addressing the complexity of an underlying STEM phenomenon. The six chapters are accompanied by useful and essential appendices and chapter-end references. Each includes new (fractional-order) ways of thinking about statistics, complexity dynamics, and what constitutes a solution to a complexity science problem. The book will appeal to students and researchers in all STEM-related fields, such as engineering, physics, biology and biomedicine, climate change, big data, and machine learning. It is also suitable for general readers interested in these fields.$

جزئیات و درخواست

By Bruce J. West, YangQuan Chen
Publisher: CRC Press, 2024-05-16
Pages: 147
Language: en
ISBN_13:9781040012697
ISBN_10:1040012698
Subject: Mathematics

Fractional Calculus for Skeptics

The fractal paradigm. I

$"This book is the first of its kind on fractional calculus (FC), dedicated to advocating for FC in STEM education and research. Fractional calculus is increasingly used today, but there remains a core population of skeptics regarding the utility of this "new" calculus. This book is intended for those who are skeptical about the need for fractional calculus to describe dynamic complex networks and must be convinced of its use on a case-by-case basis. It is a one-stop resource to rapidly read and replace the appropriate skepticism with new knowledge. It offers compelling reasons from the perspectives of the physical, social, and life sciences as to why fractional calculus is needed when addressing the complexity of an underlying STEM phenomenon. The six chapters are accompanied by useful and essential appendices and chapter-end references. Each includes new (fractional-order) ways of thinking about statistics, complexity dynamics, and what constitutes a solution to a complexity science problem. The book will appeal to students and researchers in all STEM-related fields, engineering, physics, biology and biomedicine, climate change, big data, machine learning, etc. It is also suitable for general readers interested in these fields"--$

جزئیات و درخواست

By Bruce J. West, YangQuan Chen
2024
Language: en
ISBN_10:100346856X
ISBN_13:9781003468561
Subject: Mathematics

Functional Fractional Calculus for System Identification and Controls

$In this book, not only are mathematical abstractions discussed in a lucid manner, but also several practical applications are given particularly for system identification, description and then efficient controls. The reader gets a feeling of the wide applicability of fractional calculus in the field of science and engineering. With this book, a starter can understand the concepts of this emerging field with a minimal effort and basic mathematics.$

جزئیات و درخواست

By Shantanu Das
Publisher: Springer Science & Business Media, 2007-09-26
Pages: 251
Language: en
ISBN_13:9783540727033
ISBN_10:3540727035
Subject: Technology & Engineering

Non-Integer Order Calculus and its Applications

9th International Conference on Non-Integer Order Calculus a...

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

جزئیات و درخواست

By Piotr Ostalczyk, Dominik Sankowski, Jacek Nowakowski
Publisher: Springer, 2018-03-22
Pages: 235
Language: en
ISBN_13:9783319784588
ISBN_10:3319784587
Subject: Technology & Engineering

Fractional Calculus View of Complexity

Tomorrow's Science

$This book is not a text devoted to a pedagogical presentation of a specialized topic nor is it a monograph focused on the author's area of research. It accomplishes both these things while providing a rationale for why the reader ought to be interested in learning about fractional calculus. This book is for researchers who has heard about many$

جزئیات و درخواست

By Bruce J. West
Publisher: CRC Press, 2016-01-05
Pages: 303
Language: en
ISBN_13:9781498738019
ISBN_10:149873801X
Subject: Mathematics

Introduction To The Fractional Calculus Of Variations

$This invaluable book provides a broad introduction to the fascinating and beautiful subject of Fractional Calculus of Variations (FCV). In 1996, FVC evolved in order to better describe non-conservative systems in mechanics. The inclusion of non-conservatism is extremely important from the point of view of applications. Forces that do not store energy are always present in real systems. They remove energy from the systems and, as a consequence, Noether's conservation laws cease to be valid. However, it is still possible to obtain the validity of Noether's principle using FCV. The new theory provides a more realistic approach to physics, allowing us to consider non-conservative systems in a natural way. The authors prove the necessary Euler-Lagrange conditions and corresponding Noether theorems for several types of fractional variational problems, with and without constraints, using Lagrangian and Hamiltonian formalisms. Sufficient optimality conditions are also obtained under convexity, and Leitmann's direct method is discussed within the framework of FCV.The book is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and ambitious undergraduates in mathematics and mechanics. It provides an opportunity for an introduction to FCV for experienced researchers. The explanations in the book are detailed, in order to capture the interest of the curious reader, and the book provides the necessary background material required to go further into the subject and explore the rich research literature./a$

جزئیات و درخواست

By Delfim F M Torres, Agnieszka Barbara Malinowska
Publisher: World Scientific Publishing Company, 2012-09-14
Pages: 292
Language: en
ISBN_13:9781848169685
ISBN_10:184816968X
Subject: Mathematics

Applications Of Fractional Calculus In Physics

$Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus.This volume provides an introduction to fractional calculus for physicists, and collects easily accessible review articles surveying those areas of physics in which applications of fractional calculus have recently become prominent.$

جزئیات و درخواست

By Rudolf Hilfer
Publisher: World Scientific, 2000-03-02
Pages: 473
Language: en
ISBN_13:9789814496209
ISBN_10:9814496200
Subject: Science

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

جزئیات و درخواست

Publisher: Elsevier, 1974-09-05
Pages: 252
Language: en
ISBN_13:9780080956206
ISBN_10:0080956203
Subject: Mathematics

Fractional Calculus: An Introduction For Physicists (2nd Edition)

$The book presents a concise introduction to the basic methods and strategies in fractional calculus and enables the reader to catch up with the state of the art in this field as well as to participate and contribute in the development of this exciting research area.The contents are devoted to the application of fractional calculus to physical problems. The fractional concept is applied to subjects in classical mechanics, group theory, quantum mechanics, nuclear physics, hadron spectroscopy and quantum field theory and it will surprise the reader with new intriguing insights.This new, extended edition now also covers additional chapters about image processing, folded potentials in cluster physics, infrared spectroscopy and local aspects of fractional calculus. A new feature is exercises with elaborated solutions, which significantly supports a deeper understanding of general aspects of the theory. As a result, this book should also be useful as a supporting medium for teachers and courses devoted to this subject.$

جزئیات و درخواست

By Richard Herrmann
Publisher: World Scientific, 2014-01-03
Pages: 500
Language: en
ISBN_13:9789814551090
ISBN_10:9814551090
Subject: Science

Fractional Calculus

Models and Numerical Methods

$The subject of fractional calculus and its applications (that is, convolution-type pseudo-differential operators including integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, mainly due to its applications in diverse fields of science and engineering. These operators have been used to model problems with anomalous dynamics, however, they also are an effective tool as filters and controllers, and they can be applied to write complicated functions in terms of fractional integrals or derivatives of elementary functions, and so on. This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models. All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book was written with a trade-off in mind between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. Numerical code is also provided.$

جزئیات و درخواست

By Dumitru Baleanu
Publisher: World Scientific, 2012
Pages: 426
Language: en
ISBN_13:9789814355216
ISBN_10:9814355216
Subject: Mathematics

Fractional Calculus and Its Applications

Proceedings of the International Conference held at the Univ...

جزئیات و درخواست

By B. Ross
Publisher: Springer, 2006-11-15
Pages: 391
Language: en
ISBN_13:9783540699750
ISBN_10:3540699759
Subject: Mathematics

Fractional Calculus

An Introduction for Physicists

$Fractional calculus is undergoing rapidly and ongoing development. We can already recognize, that within its framework new concepts and strategies emerge, which lead to new challenging insights and surprising correlations between different branches of physics. This book is an invitation both to the interested student and the professional researcher. It presents a thorough introduction to the basics of fractional calculus and guides the reader directly to the current state-of-the-art physical interpretation. It is also devoted to the application of fractional calculus on physical problems, in the subjects of classical mechanics, friction, damping, oscillations, group theory, quantum mechanics, nuclear physics, and hadron spectroscopy up to quantum field theory.$

جزئیات و درخواست

By Richard Herrmann
Publisher: World Scientific, 2011
Pages: 274
Language: en
ISBN_13:9789814340243
ISBN_10:9814340243
Subject: Science

Fractional Calculus: Theory and Applications

جزئیات و درخواست

By Francesco Mainardi
Publisher: MDPI, 2018-09-20
Pages: 209
Language: en
ISBN_13:9783038972068
ISBN_10:3038972061
Subject: Mathematics

Fractional Calculus with its Applications in Engineering and Technology

$This book aims to provide the basic theory of fractional calculus and its applications based on practical schemes and approaches, illustrated with applicable engineering and technical examples, especially focusing on the fractional-order controller design. In the development of this book, the essential theorems and facts in the first two chapters are proven with rigorous mathematical analyses. In addition, the commonly used definitions of Grünwald-Letnikov, Riemann-Liouville, Caputo, and Miller-Ross fractional derivatives are introduced with their properties proved and linked to fractional-order controller design. The last chapter presents several enlightening scenarios of fractional-order control designs, for example, the suppression of machining chatter, the nonlinear motion control of a multilink robot, the simultaneous tracking and stabilization control of a rotary inverted pendulum, and the idle speed control of an internal combustion engine (ICE).$

جزئیات و درخواست

By Yi Yang, Haiyan Henry Zhang
Publisher: Springer Nature, 2022-05-31
Pages: 95
Language: en
ISBN_13:9783031796258
ISBN_10:303179625X
Subject: Technology & Engineering

Handbook of Fractional Calculus for Engineering and Science

$Fractional calculus is used to model many real-life situations from science and engineering. The book includes different topics associated with such equations and their relevance and significance in various scientific areas of study and research. In this book readers will find several important and useful methods and techniques for solving various types of fractional-order models in science and engineering. The book should be useful for graduate students, PhD students, researchers and educators interested in mathematical modelling, physical sciences, engineering sciences, applied mathematical sciences, applied sciences, and so on. This Handbook: Provides reliable methods for solving fractional-order models in science and engineering. Contains efficient numerical methods and algorithms for engineering-related equations. Contains comparison of various methods for accuracy and validity. Demonstrates the applicability of fractional calculus in science and engineering. Examines qualitative as well as quantitative properties of solutions of various types of science- and engineering-related equations. Readers will find this book to be useful and valuable in increasing and updating their knowledge in this field and will be it will be helpful for engineers, mathematicians, scientist and researchers working on various real-life problems.$

جزئیات و درخواست

By Harendra Singh, H. M. Srivastava, Juan J. Nieto
Publisher: CRC Press, 2022-02-16
Pages: 318
Language: en
ISBN_13:9781000540086
ISBN_10:1000540081
Subject: Mathematics

Fractional Calculus in Medical and Health Science

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

جزئیات و درخواست

By Devendra Kumar, Jagdev Singh
Publisher: CRC Press, 2020-07-09
Pages: 153
Language: en
ISBN_13:9781000081855
ISBN_10:1000081850
Subject: Technology & Engineering

Fractional Calculus: An Introduction For Physicists (Third Edition)

$'The third edition of this book is designed to carefully and coherently introduce fractional calculus to physicists, by applying the ideas to two distinct applications: classical problems and multi-particle quantum problems. There remain many open questions and the field remains an active area of research. Dr Herrmann’s book is an excellent introduction to this field of study.'Contemporary PhysicsThe book presents a concise introduction to the basic methods and strategies in fractional calculus which enables the reader to catch up with the state-of-the-art in this field and to participate and contribute in the development of this exciting research area.This book is devoted to the application of fractional calculus on physical problems. The fractional concept is applied to subjects in classical mechanics, image processing, folded potentials in cluster physics, infrared spectroscopy, group theory, quantum mechanics, nuclear physics, hadron spectroscopy up to quantum field theory and will surprise the reader with new intriguing insights.This new, extended edition includes additional chapters about numerical solution of the fractional Schrödinger equation, self-similarity and the geometric interpretation of non-isotropic fractional differential operators. Motivated by the positive response, new exercises with elaborated solutions are added, which significantly support a deeper understanding of the general aspects of the theory.Besides students as well as researchers in this field, this book will also be useful as a supporting medium for teachers teaching courses devoted to this subject.$

جزئیات و درخواست

By Richard Herrmann
Publisher: World Scientific, 2018-07-09
Pages: 635
Language: en
ISBN_13:9789813274594
ISBN_10:981327459X
Subject: Science

Advances in Fractional Calculus

Theoretical Developments and Applications in Physics and Eng...

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

جزئیات و درخواست

By J. Sabatier, O. P. Agrawal, J. A. Tenreiro Machado
Publisher: Springer Science & Business Media, 2007-07-28
Pages: 550
Language: en
ISBN_13:9781402060427
ISBN_10:1402060424
Subject: Technology & Engineering

Generalized Fractional Calculus and Applications

جزئیات و درخواست

By Virginia S Kiryakova
Publisher: CRC Press, 1993-12-27
Pages: 412
Language: en
ISBN_10:0582219779
ISBN_13:9780582219779
Subject: Mathematics

Fractional Calculus and Fractional Differential Equations

$This book provides a broad overview of the latest developments in fractional calculus and fractional differential equations (FDEs) with an aim to motivate the readers to venture into these areas. It also presents original research describing the fractional operators of variable order, fractional-order delay differential equations, chaos and related phenomena in detail. Selected results on the stability of solutions of nonlinear dynamical systems of the non-commensurate fractional order have also been included. Furthermore, artificial neural network and fractional differential equations are elaborated on; and new transform methods (for example, Sumudu methods) and how they can be employed to solve fractional partial differential equations are discussed. The book covers the latest research on a variety of topics, including: comparison of various numerical methods for solving FDEs, the Adomian decomposition method and its applications to fractional versions of the classical Poisson processes, variable-order fractional operators, fractional variational principles, fractional delay differential equations, fractional-order dynamical systems and stability analysis, inequalities and comparison theorems in FDEs, artificial neural network approximation for fractional operators, and new transform methods for solving partial FDEs. Given its scope and level of detail, the book will be an invaluable asset for researchers working in these areas.$

جزئیات و درخواست

By Varsha Daftardar-Gejji
Publisher: Springer, 2019-08-10
Pages: 180
Language: en
ISBN_13:9789811392276
ISBN_10:9811392277
Subject: Mathematics

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