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Fractional Calculus In Bioengineering Part 2
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Book Synopsis Fractional Calculus in Bioengineering by : Richard L. Magin
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"--
Book Synopsis Advances in Fractional Calculus by : J. Sabatier
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 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.
Book Synopsis Progress in Molecular and Environmental Bioengineering by : Angelo Carpi
Download or read book Progress in Molecular and Environmental Bioengineering written by Angelo Carpi and published by BoD – Books on Demand. This book was released on 2011-08-01 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an example of the successful and rapid expansion of bioengineering within the world of the science. It includes a core of studies on bioengineering technology applications so important that their progress is expected to improve both human health and ecosystem. These studies provide an important update on technology and achievements in molecular and cellular engineering as well as in the relatively new field of environmental bioengineering. The book will hopefully attract the interest of not only the bioengineers, researchers or professionals, but also of everyone who appreciates life and environmental sciences.
Book Synopsis Fractional Calculus And Waves In Linear Viscoelasticity: An Introduction To Mathematical Models by : Francesco Mainardi
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
Book Synopsis Lung Mechanics by : Jason H. T. Bates
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.
Book Synopsis Advances in Mathematical Modelling, Applied Analysis and Computation by : Jagdev Singh
Download or read book Advances in Mathematical Modelling, Applied Analysis and Computation written by Jagdev Singh and published by Springer Nature. This book was released on 2022-10-13 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a valuable source for graduate students and researchers and provides a comprehensive introduction to recent theories and applications of mathematical modeling and numerical simulation. It includes selected peer-reviewed papers presented at the 4th International Conference on Mathematical Modelling, Applied Analysis and Computation (ICMMAAC 2021), held at JECRC University, Jaipur, India, during August 5–7, 2021. The book is focused on mathematical modeling of various problems arising in science and engineering and new efficient numerical approaches for solving linear nonlinear problems and rigorous mathematical theories, which can be used to analyze different kinds of mathematical models. Applications of mathematical methods in physics, chemistry, biology, mechanical engineering, civil engineering, computer science, social science, and finance are presented.
Book Synopsis Applications Of Fractional Calculus In Physics by : Rudolf Hilfer
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.
Book Synopsis The Analysis of Fractional Differential Equations by : Kai Diethelm
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.
Book Synopsis Introduction To The Fractional Calculus Of Variations by : Delfim F M Torres
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
Book Synopsis Fractional Calculus by : Roy Abi Zeid Daou
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.
Book Synopsis Fractional Signals and Systems by : Manuel Duarte Ortigueira
Download or read book Fractional Signals and Systems written by Manuel Duarte Ortigueira and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-03-09 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book illustrates the theoretical results of fractional derivatives via applications in signals and systems, covering continuous and discrete derivatives, and the corresponding linear systems. Both time and frequency analysis are presented. Some advanced topics are included like derivatives of stochastic processes. It is an essential reference for researchers in mathematics, physics, and engineering.
Book Synopsis The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order by :
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
Book Synopsis Automated Drug Delivery in Anesthesia by : Dana Copot
Download or read book Automated Drug Delivery in Anesthesia written by Dana Copot and published by Academic Press. This book was released on 2020-04-29 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automated Drug Delivery in Anesthesia provides a full review of available tools and methods on the drug delivery of anesthesia, bridging the gap between academic development, research and clinical practice. The book takes an interdisciplinary approach, pulling information about tools developed in other disciplines such as mathematics, physics, biology and system engineering and applying them to drug delivery. The book's authors discuss the missing element of complete regulatory loop of anesthesia: the sensor and model for pain pathway assessment. This is the only book which focuses specifically on the delivery of anesthesia. - Revisits the standard TCI anesthesia regulatory loop - Provides complementary measurement devices and protocols for hypnosis, analgesia and neuromuscular blockade (the three components for anesthesia) - Describes the link between existing and emerging tools
Book Synopsis General Fractional Derivatives by : Xiao-Jun Yang
Download or read book General Fractional Derivatives written by Xiao-Jun Yang and published by CRC Press. This book was released on 2019-05-10 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: General Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional derivatives, fractional integrals, general fractional derivatives, and general fractional integrals of the constant and variable order without and with respect to another function due to the appearance of the power-law and complex herbivores to figure out the modern developments in theoretical and applied science. Features: Give some new results for fractional calculus of constant and variable orders. Discuss some new definitions for fractional calculus with respect to another function. Provide definitions for general fractional calculus of constant and variable orders. Report new results of general fractional calculus with respect to another function. Propose news special functions with respect to another function and their applications. Present new models for the anomalous relaxation and rheological behaviors. This book serves as a reference book and textbook for scientists and engineers in the fields of mathematics, physics, chemistry and engineering, senior undergraduate and graduate students. Dr. Xiao-Jun Yang is a full professor of Applied Mathematics and Mechanics, at China University of Mining and Technology, China. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Modelling and Analysis, International Journal of Numerical Methods for Heat & Fluid Flow, and Thermal Science.
Book Synopsis Information Technology and Applied Mathematics by : Peeyush Chandra
Download or read book Information Technology and Applied Mathematics written by Peeyush Chandra and published by Springer. This book was released on 2018-05-08 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses recent advances and contemporary research in the field of cryptography, security, mathematics and statistics, and their applications in computing and information technology. Mainly focusing on mathematics and applications of mathematics in computer science and information technology, it includes contributions from eminent international scientists, researchers, and scholars. The book helps researchers update their knowledge of cryptography, security, algebra, frame theory, optimizations, stochastic processes, compressive sensing, functional analysis, and complex variables.
Book Synopsis Fractal Physiology by : James B Bassingthwaighte
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.
