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)

Author: Francesco Mainardi

Publisher: World Scientific

Published: 2022-08-16

Total Pages: 626

ISBN-13: 1783264004

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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 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.

Fractional Calculus

Fractional Calculus

Author: Dumitru Baleanu

Publisher: World Scientific

Published: 2012

Total Pages: 426

ISBN-13: 9814355208

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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.


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.

Basic Theory

Basic Theory

Author: Anatoly Kochubei

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2019-02-19

Total Pages: 752

ISBN-13: 3110570637

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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 Basic Theory by : Anatoly Kochubei

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.

Fractional Calculus

Fractional Calculus

Author: Richard Herrmann

Publisher: World Scientific

Published: 2011-02-21

Total Pages: 276

ISBN-13: 9814462071

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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 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

Fractional Calculus with Applications in Mechanics

Fractional Calculus with Applications in Mechanics

Author: Teodor M. Atanackovic

Publisher: John Wiley & Sons

Published: 2014-02-19

Total Pages: 437

ISBN-13: 1118909135

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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 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 437 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.

Fractional Calculus with Applications in Mechanics

Fractional Calculus with Applications in Mechanics

Author: Teodor M. Atanackovic

Publisher: John Wiley & Sons

Published: 2014-03-17

Total Pages: 437

ISBN-13: 1848216793

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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 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 2014-03-17 with total page 437 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.

The Analysis of Fractional Differential Equations

The Analysis of Fractional Differential Equations

Author: Kai Diethelm

Publisher: Springer

Published: 2010-08-18

Total Pages: 251

ISBN-13: 3642145744

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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 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.

Three Plays of Maureen Hunter

Three Plays of Maureen Hunter

Author: Hunter, Maureen

Publisher: OIBooks-Libros

Published: 2003

Total Pages: 944

ISBN-13: 1896239994

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


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

Economic Dynamics with Memory

Economic Dynamics with Memory

Author: Vasily E. Tarasov

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2021-01-18

Total Pages: 602

ISBN-13: 3110627450

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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 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.

Special Functions in Fractional Calculus and Engineering

Special Functions in Fractional Calculus and Engineering

Author: Harendra Singh

Publisher: CRC Press

Published: 2023-06-29

Total Pages: 315

ISBN-13: 1000899756

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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 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.