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Fractional Calculus And Waves In Linear Viscoelasticity An Introduction To Mathematical Models Second Edition
Download Fractional Calculus And Waves In Linear Viscoelasticity An Introduction To Mathematical Models Second Edition full books in PDF, epub, and Kindle. Read online Fractional Calculus And Waves In Linear Viscoelasticity An Introduction To Mathematical Models Second Edition ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Fractional Calculus And Waves In Linear Viscoelasticity: An Introduction To Mathematical Models (Second Edition) by : Francesco Mainardi
Download or read book Fractional Calculus And Waves In Linear Viscoelasticity: An Introduction To Mathematical Models (Second Edition) written by Francesco Mainardi and published by World Scientific. This book was released on 2022-08-16 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional Calculus and Waves in Linear Viscoelasticity (Second Edition) is a self-contained treatment of the mathematical theory of linear (uni-axial) viscoelasticity (constitutive equation and waves) with particular regard to models based on fractional calculus. It serves 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. In particular the relevant role played by some special functions is pointed out along with their visualization through plots. Graphics are extensively used in the book and a large general bibliography is included at the end.This new edition keeps the structure of the first edition but each chapter has been revised and expanded, and new additions include a novel appendix on complete monotonic and Bernstein functions that are known to play a fundamental role in linear viscoelasticity.This book is suitable for engineers, graduate students and researchers interested in fractional calculus and continuum mechanics.
Book Synopsis Fractional Calculus by : Dumitru Baleanu
Download or read book Fractional Calculus written by Dumitru Baleanu and published by World Scientific. This book was released on 2012 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title 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.
Download or read book Basic Theory written by Anatoly Kochubei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fractional Calculus by : Richard Herrmann
Download or read book Fractional Calculus written by Richard Herrmann and published by World Scientific. This book was released on 2011-02-21 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus is undergoing rapid 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. Contents:FunctionsThe Fractional DerivativeFriction ForcesFractional CalculusThe Fractional Harmonic OscillatorWave Equations and ParityNonlocality and Memory EffectsQuantum MechanicsFractional Spin: A Property of Particles Described with the Fractional Schrödinger EquationFactorizationSymmetriesThe Fractional Symmetric Rigid Rotorq-Deformed Lie Algebras and Fractional CalculusFractional Spectroscopy of HadronsHigher Dimensional Fractional Rotation GroupsFractors: Fractional Tensor CalculusFractional FieldsGauge Invariance in Fractional Field TheoriesOutlook Readership: Students and researchers in physics. Keywords:Fractional Calculus;Fractional Group Theory;Fractional Lie-Algebras;Nuclear Physics;Fractional Friction;Fractional Harmonic Oscillator;Fractional Spin;Fractional Rotation Group;Memory-Effects;Causality;Nonlocal Field Theories;Fractors;Fractional Tensor Calculus;Fractional Fields;Gauge Fields;Fractional Differential Equations;Particle PhysicsKey Features:A thorough introduction to the basics of fractional calculus leading the reader up to the state-of-the-art physical interpretationWhat makes this textbook unique is its application-oriented approach. All derived results are directly compared to experimental findings and the superior generalized view of a fractional approach is demonstrated leading to intriguing new insightsThe reader is guided on a solid basis and is encouraged to apply the fractional calculus approach in his own research area tooReviews: “Fractional Calculus is an affordable and valuable introduction to the field that will appeal to physicists interested in scientific what-ifs.” Physics Today “… the first three chapters actually appear very helpful at the graduate level. Each chapter has a careful precis at the start. There a many analyses illustrating outcomes of fractional analyses… If this [fractional calculus] is the field of your research then this book is essential with numerous references… ” Contemporary Physics “The book has the property that derived results are directly compared with experimental findings. As a consequence, the reader is guided and encouraged to apply the fractional calculus approach in her/his research area. The reviewer strongly recommends this book for beginners as well as specialists in the fields of physics, mathematics and complex adaptive systems.” Zentralblatt MATH
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 247 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 Fractional Calculus with Applications in Mechanics by : Teodor M. Atanackovic
Download or read book Fractional Calculus with Applications in Mechanics written by Teodor M. Atanackovic and published by John Wiley & Sons. This book was released on 2014-02-19 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: The books Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes and Fractional Calculus with Applications in Mechanics: Wave Propagation, Impact and Variational Principles contain various applications of fractional calculus to the fields of classical mechanics. Namely, the books study problems in fields such as viscoelasticity of fractional order, lateral vibrations of a rod of fractional order type, lateral vibrations of a rod positioned on fractional order viscoelastic foundations, diffusion-wave phenomena, heat conduction, wave propagation, forced oscillations of a body attached to a rod, impact and variational principles of a Hamiltonian type. The books will be useful for graduate students in mechanics and applied mathematics, as well as for researchers in these fields. Part 1 of this book presents an introduction to fractional calculus. Chapter 1 briefly gives definitions and notions that are needed later in the book and Chapter 2 presents definitions and some of the properties of fractional integrals and derivatives. Part 2 is the central part of the book. Chapter 3 presents the analysis of waves in fractional viscoelastic materials in infinite and finite spatial domains. In Chapter 4, the problem of oscillations of a translatory moving rigid body, attached to a heavy, or light viscoelastic rod of fractional order type, is studied in detail. In Chapter 5, the authors analyze a specific engineering problem of the impact of a viscoelastic rod against a rigid wall. Finally, in Chapter 6, some results for the optimization of a functional containing fractional derivatives of constant and variable order are presented.
Book Synopsis Three Plays of Maureen Hunter by : Hunter, Maureen
Download or read book Three Plays of Maureen Hunter written by Hunter, Maureen and published by OIBooks-Libros. This book was released on 2003 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: Book is clean and tight. No writing in text. Like New
Book Synopsis Abel Integral Equations by : Rudolf Gorenflo
Download or read book Abel Integral Equations written by Rudolf Gorenflo and published by Springer. This book was released on 2006-11-14 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many fields of application of mathematics, progress is crucially dependent on the good flow of information between (i) theoretical mathematicians looking for applications, (ii) mathematicians working in applications in need of theory, and (iii) scientists and engineers applying mathematical models and methods. The intention of this book is to stimulate this flow of information. In the first three chapters (accessible to third year students of mathematics and physics and to mathematically interested engineers) applications of Abel integral equations are surveyed broadly including determination of potentials, stereology, seismic travel times, spectroscopy, optical fibres. In subsequent chapters (requiring some background in functional analysis) mapping properties of Abel integral operators and their relation to other integral transforms in various function spaces are investi- gated, questions of existence and uniqueness of solutions of linear and nonlinear Abel integral equations are treated, and for equations of the first kind problems of ill-posedness are discussed. Finally, some numerical methods are described. In the theoretical parts, emphasis is put on the aspects relevant to applications.
Book Synopsis Economic Dynamics with Memory by : Vasily E. Tarasov
Download or read book Economic Dynamics with Memory written by Vasily E. Tarasov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-01-18 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the applications of fractional calculus, fractional operators of non-integer orders and fractional differential equations in describing economic dynamics with long memory. Generalizations of basic economic concepts, notions and methods for the economic processes with memory are suggested. New micro and macroeconomic models with continuous time are proposed to describe the fractional economic dynamics with long memory as well.
Book Synopsis Special Functions in Fractional Calculus and Engineering by : Harendra Singh
Download or read book Special Functions in Fractional Calculus and Engineering written by Harendra Singh and published by CRC Press. This book was released on 2023-06-29 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special functions play a very important role in solving various families of ordinary and partial differential equations as well as their fractional-order analogs, which model real-life situations. Owing to the non-local nature and memory effect, fractional calculus is capable of modeling many situations which arise in engineering. This book includes a collection of related topics associated with such equations and their relevance and significance in engineering. Special Functions in Fractional Calculus and Engineering highlights the significance and applicability of special functions in solving fractional-order differential equations with engineering applications. This book focuses on the non-local nature and memory effect of fractional calculus in modeling relevant to engineering science and covers a variety of important and useful methods using special functions for solving various types of fractional-order models relevant to engineering science. This book goes on to illustrate the applicability and usefulness of special functions by justifying their numerous and widespread occurrences in the solution of fractional-order differential, integral, and integrodifferential equations. This book holds a wide variety of interconnected fundamental and advanced topics with interdisciplinary applications that combine applied mathematics and engineering sciences, which are useful to graduate students, Ph.D. scholars, researchers, and educators interested in special functions, fractional calculus, mathematical modeling, and engineering.
Book Synopsis Fractional Differential Equations by : Anatoly Kochubei
Download or read book Fractional Differential Equations written by Anatoly Kochubei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.
Book Synopsis Integral Methods in Science and Engineering by : Christian Constanda
Download or read book Integral Methods in Science and Engineering written by Christian Constanda and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in science and technology are driven by the development of rigorous mathematical foundations for the study of both theoretical and experimental models. With certain methodological variations, this type of study always comes down to the application of analytic or computational integration procedures, making such tools indispensible. With a wealth of cutting-edge research in the field, Integral Methods in Science and Engineering: Progress in Numerical and Analytic Techniques provides a detailed portrait of both the construction of theoretical integral techniques and their application to specific problems in science and engineering. The chapters in this volume are based on talks given by well-known researchers at the Twelfth International Conference on Integral Methods in Science and Engineering, July 23–27, 2012, in Porto Alegre, Brazil. They address a broad range of topics, from problems of existence and uniqueness for singular integral equations on domain boundaries to numerical integration via finite and boundary elements, conservation laws, hybrid methods, and other quadrature-related approaches. The contributing authors bring their expertise to bear on a number of topical problems that have to date resisted solution, thereby offering help and guidance to fellow professionals worldwide. Integral Methods in Science and Engineering: Progress in Numerical and Analytic Techniques will be a valuable resource for researchers in applied mathematics, physics, and mechanical and electrical engineering, for graduate students in these disciplines, and for various other professionals who use integration as an essential tool in their work.
Book Synopsis Frontiers in Fractional Calculus by : Sachin Bhalekar
Download or read book Frontiers in Fractional Calculus written by Sachin Bhalekar and published by Bentham Science Publishers. This book was released on 2018-03-21 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together eleven topics on different aspects of fractional calculus in a single volume. It provides readers the basic knowledge of fractional calculus and introduces advanced topics and applications. The information in the book is presented in four parts: 1. Fractional Diffusion Equations: (i) solutions of fractional diffusion equations using wavelet methods, (ii) the maximum principle for time fractional diffusion equations, (iii) nonlinear sub-diffusion equations. 2. Mathematical Analysis: (i) shifted Jacobi polynomials for solving and identifying coupled fractional delay differential equations, (ii) the monotone iteration principle in the theory of Hadamard fractional delay differential equations, (iii) dynamics of fractional order modified Bhalekar-Gejji System, (iv) Grunwald-Letnikov derivatives. 3. Computational Techniques: GPU computing of special mathematical functions used in fractional calculus. 4. Reviews: (i) the popular iterative method NIM, (ii) fractional derivative with non-singular kernels, (iii) some open problems in fractional order nonlinear system This is a useful reference for researchers and graduate level mathematics students seeking knowledge about of fractional calculus and applied mathematics.
Book Synopsis Fractional Calculus by : Dumitru Baleanu
Download or read book Fractional Calculus written by Dumitru Baleanu and published by World Scientific. This book was released on 2012 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fixed Point Theory and Fractional Calculus by : Pradip Debnath
Download or read book Fixed Point Theory and Fractional Calculus written by Pradip Debnath and published by Springer Nature. This book was released on 2022-05-10 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects chapters on fixed-point theory and fractional calculus and their applications in science and engineering. It discusses state-of-the-art developments in these two areas through original new contributions from scientists across the world. It contains several useful tools and techniques to develop their skills and expertise in fixed-point theory and fractional calculus. New research directions are also indicated in chapters. This book is meant for graduate students and researchers willing to expand their knowledge in these areas. The minimum prerequisite for readers is the graduate-level knowledge of analysis, topology and functional analysis.
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 298 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 Solved Exercises in Fractional Calculus by : Edmundo Capelas de Oliveira
Download or read book Solved Exercises in Fractional Calculus written by Edmundo Capelas de Oliveira and published by Springer. This book was released on 2019-05-31 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a brief historical introduction and state of the art in fractional calculus. The author introduces some of the so-called special functions, in particular, those which will be directly involved in calculations. The concepts of fractional integral and fractional derivative are also presented. Each chapter, except for the first one, contains a list of exercises containing suggestions for solving them and at last the resolution itself. At the end of those chapters there is a list of complementary exercises. The last chapter presents several applications of fractional calculus.
