Download or read book FRACTIONAL CALCULUS IN BIOENGINEERING PART 1 written by R. MAGIN and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fractional Calculus in Bioengineering written by Richard L. Magin and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is written for bioengineers who wish to learn more about fractional calculus (integration and differentiation of arbitrary order) and the ways in which it can be used to solve biomedical problems. However, the text covers a wide range of topics (bioelectrodes, biomaterials, neural networks, etc.) that I hope will be of interest to other scientists and engineers as well as to bioengineers. Examples and exercises show that with only a small change in notation and perspective, fractional calculus extends many of the modeling capabilities of conventional calculus and integer order differential equations. By combining an "engineer's" approach to fractional calculus - largely through using the Laplace transform - with examples taken from a variety of biomedical applications, this book will help new students learn to use the techniques of fractional calculus. The second edition of this book contains updates and corrections to equations and descriptions from the first edition"--
Download or read book Fractional Calculus in Bioengineering written by Richard L. Magin and published by . This book was released on 2006-01-01 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fractional Calculus for Scientists and Engineers written by Manuel Duarte Ortigueira and published by Springer Science & Business Media. This book was released on 2011-06-02 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a practical overview of Fractional Calculus as it relates to Signal Processing
Download or read book Fractional Calculus written by Roy Abi Zeid Daou and published by Nova Science Publishers. This book was released on 2014-01-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Analysis of Fractional Differential Equations written by Kai Diethelm and published by Springer. This book was released on 2010-08-18 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.
Download or read book Applications Of Fractional Calculus In Physics written by Rudolf Hilfer and published by World Scientific. This book was released on 2000-03-02 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fractional Differential Equations written by Igor Podlubny and published by Elsevier. This book was released on 1998-10-27 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'.This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models.In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research.A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications. - A unique survey of many applications of fractional calculus - Presents basic theory - Includes a unified presentation of selected classical results, which are important for applications - Provides many examples - Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory - The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches - Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives
Download or read book Fractional Calculus And Waves In Linear Viscoelasticity An Introduction To Mathematical Models written by Francesco Mainardi and published by World Scientific. This book was released on 2010-05-18 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a comprehensive overview of the author's work on the fields of fractional calculus and waves in linear viscoelastic media, which includes his pioneering contributions on the applications of special functions of the Mittag-Leffler and Wright types.It is intended to serve as a general introduction to the above-mentioned areas of mathematical modeling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature given in the huge general bibliography.This book is likely to be of interest to applied scientists and engineers./a
Download or read book Fractal Physiology written by James B Bassingthwaighte and published by Springer. This book was released on 2013-05-27 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: I know that most men, including those at ease with the problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives. Joseph Ford quoting Tolstoy (Gleick, 1987) We are used to thinking that natural objects have a certain form and that this form is determined by a characteristic scale. If we magnify the object beyond this scale, no new features are revealed. To correctly measure the properties of the object, such as length, area, or volume, we measure it at a resolution finer than the characteristic scale of the object. We expect that the value we measure has a unique value for the object. This simple idea is the basis of the calculus, Euclidean geometry, and the theory of measurement. However, Mandelbrot (1977, 1983) brought to the world's attention that many natural objects simply do not have this preconceived form. Many of the structures in space and processes in time of living things have a very different form. Living things have structures in space and fluctuations in time that cannot be characterized by one spatial or temporal scale. They extend over many spatial or temporal scales.
Download or read book Functional Calculus written by Kamal Shah and published by BoD – Books on Demand. This book was released on 2020-06-17 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present a broad overview of the theory and applications related to functional calculus. The book is based on two main subject areas: matrix calculus and applications of Hilbert spaces. Determinantal representations of the core inverse and its generalizations, new series formulas for matrix exponential series, results on fixed point theory, and chaotic graph operations and their fundamental group are contained under the umbrella of matrix calculus. In addition, numerical analysis of boundary value problems of fractional differential equations are also considered here. In addition, reproducing kernel Hilbert spaces, spectral theory as an application of Hilbert spaces, and an analysis of PM10 fluctuations and optimal control are all contained in the applications of Hilbert spaces. The concept of this book covers topics that will be of interest not only for students but also for researchers and professors in this field of mathematics. The authors of each chapter convey a strong emphasis on theoretical foundations in this book.
Download or read book The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order written by and published by Elsevier. This book was released on 1974-09-05 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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; andmethods 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 particularbranches, 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
Download or read book Introduction To The Fractional Calculus Of Variations written by Delfim F M Torres and published by World Scientific Publishing Company. This book was released on 2012-09-14 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Fractional Order Design written by Ahmed G. Radwan and published by Academic Press. This book was released on 2021-10-22 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Advances in Fractional Calculus written by J. Sabatier and published by Springer Science & Business Media. This book was released on 2007-07-28 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lung Mechanics written by Jason H. T. Bates and published by Cambridge University Press. This book was released on 2009-07-30 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern quantitative study of lung mechanics, relating mathematical modeling and engineering principles to lung function, structure, mechanics, and disease.
Download or read book Stabilization and Control of Fractional Order Systems A Sliding Mode Approach written by Bijnan Bandyopadhyay and published by Springer. This book was released on 2014-07-22 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last two decades fractional differential equations have been used more frequently in physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, electro chemistry and many others. It opens a new and more realistic way to capture memory dependent phenomena and irregularities inside the systems by using more sophisticated mathematical analysis. This monograph is based on the authors’ work on stabilization and control design for continuous and discrete fractional order systems. The initial two chapters and some parts of the third chapter are written in tutorial fashion, presenting all the basic concepts of fractional order system and a brief overview of sliding mode control of fractional order systems. The other parts contain deal with robust finite time stability of fractional order systems, integral sliding mode control of fractional order systems, co-operative control of multi-agent systems modeled as fractional differential equation, robust stabilization of discrete fractional order systems, high performance control using soft variable structure control and contraction analysis by integer and fractional order infinitesimal variations.
