Fractional Calculus And Waves In Linear Viscoelasticity An Introduction To Mathematical Models Second Edition

Fractional Calculus And Waves In Linear Viscoelasticity An Introduction To Mathematical Models Second Edition Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Fractional Calculus And Waves In Linear Viscoelasticity An Introduction To Mathematical Models Second Edition book. This book definitely worth reading, it is an incredibly well-written.

Fractional Calculus And Waves In Linear Viscoelasticity: An Introduction To Mathematical Models (Second Edition)

Francesco Mainardi
Fractional Calculus And Waves In Linear Viscoelasticity An Introduction To Mathematical Models Second Edition Book PDF

Author : Francesco Mainardi
Publisher : World Scientific
Page : 626 pages
File Size : 54,5 Mb
Release : 2022-08-16
Category : Mathematics
ISBN : 9781783264001

Get Book

Fractional Calculus And Waves In Linear Viscoelasticity: An Introduction To Mathematical Models (Second Edition) by Francesco Mainardi Pdf

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.

Fractional Calculus with Applications in Mechanics

Teodor M. Atanackovic,Stevan Pilipovic,Bogoljub Stankovic,Dusan Zorica
Fractional Calculus with Applications in Mechanics Book PDF

Author : Teodor M. Atanackovic,Stevan Pilipovic,Bogoljub Stankovic,Dusan Zorica
Publisher : John Wiley & Sons
Page : 421 pages
File Size : 43,9 Mb
Release : 2014-02-19
Category : Mathematics
ISBN : 9781118909133

Get Book

Fractional Calculus with Applications in Mechanics by Teodor M. Atanackovic,Stevan Pilipovic,Bogoljub Stankovic,Dusan Zorica Pdf

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.

Basic Theory

Anatoly Kochubei,Yuri Luchko
Basic Theory Book PDF

Author : Anatoly Kochubei,Yuri Luchko
Publisher : Walter de Gruyter GmbH & Co KG
Page : 752 pages
File Size : 51,5 Mb
Release : 2019-02-19
Category : Mathematics
ISBN : 9783110570632

Get Book

Basic Theory by Anatoly Kochubei,Yuri Luchko Pdf

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.

Fractional Calculus

Richard Herrmann
Fractional Calculus Book PDF

Author : Richard Herrmann
Publisher : World Scientific
Page : 276 pages
File Size : 43,6 Mb
Release : 2011-02-21
Category : Science
ISBN : 9789814462075

Get Book

Fractional Calculus by Richard Herrmann Pdf

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

Three Plays of Maureen Hunter

Hunter, Maureen
Three Plays of Maureen Hunter Book PDF

Author : Hunter, Maureen
Publisher : OIBooks-Libros
Page : 944 pages
File Size : 52,7 Mb
Release : 2003
Category : Drama
ISBN : 9781896239996

Get Book

Three Plays of Maureen Hunter by Hunter, Maureen Pdf

Book is clean and tight. No writing in text. Like New

Economic Dynamics with Memory

Vasily E. Tarasov,Valentina V. Tarasova
Economic Dynamics with Memory Book PDF

Author : Vasily E. Tarasov,Valentina V. Tarasova
Publisher : Walter de Gruyter GmbH & Co KG
Page : 602 pages
File Size : 55,8 Mb
Release : 2021-01-18
Category : Business & Economics
ISBN : 9783110627459

Get Book

Economic Dynamics with Memory by Vasily E. Tarasov,Valentina V. Tarasova Pdf

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.

Special Functions in Fractional Calculus and Engineering

Harendra Singh,H M Srivastava,R. K. Pandey
Special Functions in Fractional Calculus and Engineering Book PDF

Author : Harendra Singh,H M Srivastava,R. K. Pandey
Publisher : CRC Press
Page : 315 pages
File Size : 46,5 Mb
Release : 2023-06-29
Category : Technology & Engineering
ISBN : 9781000899757

Get Book

Special Functions in Fractional Calculus and Engineering by Harendra Singh,H M Srivastava,R. K. Pandey Pdf

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.

Integral Methods in Science and Engineering

Christian Constanda,Bardo E.J. Bodmann,Haroldo F. de Campos Velho
Integral Methods in Science and Engineering Book PDF

Author : Christian Constanda,Bardo E.J. Bodmann,Haroldo F. de Campos Velho
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 50,5 Mb
Release : 2013-08-13
Category : Mathematics
ISBN : 9781461478287

Get Book

Integral Methods in Science and Engineering by Christian Constanda,Bardo E.J. Bodmann,Haroldo F. de Campos Velho Pdf

​​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.​

General Fractional Derivatives with Applications in Viscoelasticity

Xiao-Jun Yang,Feng Gao,Yang Ju
General Fractional Derivatives with Applications in Viscoelasticity Book PDF

Author : Xiao-Jun Yang,Feng Gao,Yang Ju
Publisher : Academic Press
Page : 456 pages
File Size : 40,7 Mb
Release : 2020-04-03
Category : Mathematics
ISBN : 9780128172094

Get Book

General Fractional Derivatives with Applications in Viscoelasticity by Xiao-Jun Yang,Feng Gao,Yang Ju Pdf

General Fractional Derivatives with Applications in Viscoelasticity introduces the newly established fractional-order calculus operators involving singular and non-singular kernels with applications to fractional-order viscoelastic models from the calculus operator viewpoint. Fractional calculus and its applications have gained considerable popularity and importance because of their applicability to many seemingly diverse and widespread fields in science and engineering. Many operations in physics and engineering can be defined accurately by using fractional derivatives to model complex phenomena. Viscoelasticity is chief among them, as the general fractional calculus approach to viscoelasticity has evolved as an empirical method of describing the properties of viscoelastic materials. General Fractional Derivatives with Applications in Viscoelasticity makes a concise presentation of general fractional calculus. Presents a comprehensive overview of the fractional derivatives and their applications in viscoelasticity Provides help in handling the power-law functions Introduces and explores the questions about general fractional derivatives and its applications

Frontiers in Fractional Calculus

Sachin Bhalekar
Frontiers in Fractional Calculus Book PDF

Author : Sachin Bhalekar
Publisher : Bentham Science Publishers
Page : 381 pages
File Size : 54,9 Mb
Release : 2018-03-21
Category : Mathematics
ISBN : 9781681085999

Get Book

Frontiers in Fractional Calculus by Sachin Bhalekar Pdf

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.

Fractional Calculus

Dumitru Baleanu
Fractional Calculus Book PDF

Author : Dumitru Baleanu
Publisher : World Scientific
Page : 426 pages
File Size : 54,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814355216

Get Book

Fractional Calculus by Dumitru Baleanu Pdf

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.

Fixed Point Theory and Fractional Calculus

Pradip Debnath,H. M. Srivastava,Poom Kumam,Bipan Hazarika
Fixed Point Theory and Fractional Calculus Book PDF

Author : Pradip Debnath,H. M. Srivastava,Poom Kumam,Bipan Hazarika
Publisher : Springer Nature
Page : 358 pages
File Size : 54,9 Mb
Release : 2022-05-10
Category : Mathematics
ISBN : 9789811906688

Get Book

Fixed Point Theory and Fractional Calculus by Pradip Debnath,H. M. Srivastava,Poom Kumam,Bipan Hazarika Pdf

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.

Fractional Signals and Systems

Manuel Duarte Ortigueira,Duarte Valério
Fractional Signals and Systems Book PDF

Author : Manuel Duarte Ortigueira,Duarte Valério
Publisher : Walter de Gruyter GmbH & Co KG
Page : 298 pages
File Size : 40,6 Mb
Release : 2020-03-09
Category : Mathematics
ISBN : 9783110624588

Get Book

Fractional Signals and Systems by Manuel Duarte Ortigueira,Duarte Valério Pdf

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.

Solved Exercises in Fractional Calculus

Edmundo Capelas de Oliveira
Solved Exercises in Fractional Calculus Book PDF

Author : Edmundo Capelas de Oliveira
Publisher : Springer
Page : 321 pages
File Size : 55,6 Mb
Release : 2019-05-31
Category : Technology & Engineering
ISBN : 9783030205249

Get Book

Solved Exercises in Fractional Calculus by Edmundo Capelas de Oliveira Pdf

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.

Handbook of Fractional Calculus for Engineering and Science

Harendra Singh,H. M. Srivastava,Juan J. Nieto
Handbook of Fractional Calculus for Engineering and Science Book PDF

Author : Harendra Singh,H. M. Srivastava,Juan J. Nieto
Publisher : CRC Press
Page : 318 pages
File Size : 45,7 Mb
Release : 2022-02-16
Category : Mathematics
ISBN : 9781000540086

Get Book

Handbook of Fractional Calculus for Engineering and Science by Harendra Singh,H. M. Srivastava,Juan J. Nieto Pdf

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.