Fractional Calculus And Waves In Linear Viscoelasticity

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

Author : Francesco Mainardi
Publisher : World Scientific
ISBN 13 : 1783264004
Total Pages : 626 pages
Book Rating : 4.7/5 (832 download)

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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: Theory and Applications

Author : Francesco Mainardi
Publisher : MDPI
ISBN 13 : 3038972061
Total Pages : 209 pages
Book Rating : 4.0/5 (389 download)

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Book Synopsis Fractional Calculus: Theory and Applications by : Francesco Mainardi

Download or read book Fractional Calculus: Theory and Applications written by Francesco Mainardi and published by MDPI. This book was released on 2018-09-20 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Fractional Calculus: Theory and Applications" that was published in Mathematics

Mathematical Problems in Linear Viscoelasticity

Author : Mauro Fabrizio
Publisher : SIAM
ISBN 13 : 0898712661
Total Pages : 210 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Mathematical Problems in Linear Viscoelasticity by : Mauro Fabrizio

Download or read book Mathematical Problems in Linear Viscoelasticity written by Mauro Fabrizio and published by SIAM. This book was released on 1992-01-01 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes general mathematical modeling of viscoelastic materials as systems with fading memory. Discusses the interrelation between topics such as existence, uniqueness, and stability of initial boundary value problems, variational and extremum principles, and wave propagation. Demonstrates the deep connection between the properties of the solution to initial boundary value problems and the requirements of the general physical principles. Discusses special techniques and new methods, including Fourier and Laplace transforms, extremum principles via weight functions, and singular surfaces and discontinuity waves.

The Analysis of Fractional Differential Equations

Author : Kai Diethelm
Publisher : Springer
ISBN 13 : 3642145744
Total Pages : 251 pages
Book Rating : 4.6/5 (421 download)

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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.

Fractional Differential Equations

Author : Anatoly Kochubei
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110571668
Total Pages : 528 pages
Book Rating : 4.1/5 (15 download)

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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.

Fractional Calculus

Author : Dumitru Baleanu
Publisher : World Scientific
ISBN 13 : 9814355208
Total Pages : 426 pages
Book Rating : 4.8/5 (143 download)

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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.

Fractional Thermoelasticity

Author : Yuriy Povstenko
Publisher : Springer Nature
ISBN 13 : 3031645871
Total Pages : 457 pages
Book Rating : 4.0/5 (316 download)

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Book Synopsis Fractional Thermoelasticity by : Yuriy Povstenko

Download or read book Fractional Thermoelasticity written by Yuriy Povstenko and published by Springer Nature. This book was released on with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advances in Applied Mathematics and Approximation Theory

Author : George A. Anastassiou
Publisher : Springer Science & Business Media
ISBN 13 : 1461463939
Total Pages : 494 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Advances in Applied Mathematics and Approximation Theory by : George A. Anastassiou

Download or read book Advances in Applied Mathematics and Approximation Theory written by George A. Anastassiou and published by Springer Science & Business Media. This book was released on 2014-07-08 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Applied Mathematics and Approximation Theory: Contributions from AMAT 2012 is a collection of the best articles presented at “Applied Mathematics and Approximation Theory 2012,” an international conference held in Ankara, Turkey, May 17-20, 2012. This volume brings together key work from authors in the field covering topics such as ODEs, PDEs, difference equations, applied analysis, computational analysis, signal theory, positive operators, statistical approximation, fuzzy approximation, fractional analysis, semigroups, inequalities, special functions and summability. The collection will be a useful resource for researchers in applied mathematics, engineering and statistics.

Waves with Power-Law Attenuation

Author : Sverre Holm
Publisher : Springer
ISBN 13 : 3030149277
Total Pages : 338 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Waves with Power-Law Attenuation by : Sverre Holm

Download or read book Waves with Power-Law Attenuation written by Sverre Holm and published by Springer. This book was released on 2019-04-15 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book integrates concepts from physical acoustics with those from linear viscoelasticity and fractional linear viscoelasticity. Compressional waves and shear waves in applications such as medical ultrasound, elastography, and sediment acoustics often follow power law attenuation and dispersion laws that cannot be described with classical viscous and relaxation models. This is accompanied by temporal power laws rather than the temporal exponential responses of classical models. The book starts by reformulating the classical models of acoustics in terms of standard models from linear elasticity. Then, non-classical loss models that follow power laws and which are expressed via convolution models and fractional derivatives are covered in depth. In addition, parallels are drawn to electromagnetic waves in complex dielectric media. The book also contains historical vignettes and important side notes about the validity of central questions. While addressed primarily to physicists and engineers working in the field of acoustics, this expert monograph will also be of interest to mathematicians, mathematical physicists, and geophysicists.

Continuum Mechanics through the Ages - From the Renaissance to the Twentieth Century

Author : Gérard A. Maugin
Publisher : Springer
ISBN 13 : 3319265938
Total Pages : 312 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Continuum Mechanics through the Ages - From the Renaissance to the Twentieth Century by : Gérard A. Maugin

Download or read book Continuum Mechanics through the Ages - From the Renaissance to the Twentieth Century written by Gérard A. Maugin and published by Springer. This book was released on 2015-11-19 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixing scientific, historic and socio-economic vision, this unique book complements two previously published volumes on the history of continuum mechanics from this distinguished author. In this volume, Gérard A. Maugin looks at the period from the renaissance to the twentieth century and he includes an appraisal of the ever enduring competition between molecular and continuum modelling views. Chapters trace early works in hydraulics and fluid mechanics not covered in the other volumes and the author investigates experimental approaches, essentially before the introduction of a true concept of stress tensor. The treatment of such topics as the viscoelasticity of solids and plasticity, fracture theory, and the role of geometry as a cornerstone of the field, are all explored. Readers will find a kind of socio-historical appraisal of the seminal contributions by our direct masters in the second half of the twentieth century. The analysis of the teaching and research texts by Duhem, Poincaré and Hilbert on continuum mechanics is key: these provide the most valuable documentary basis on which a revival of continuum mechanics and its formalization were offered in the late twentieth century. Altogether, the three volumes offer a generous conspectus of the developments of continuum mechanics between the sixteenth century and the dawn of the twenty-first century. Mechanical engineers, applied mathematicians and physicists alike will all be interested in this work which appeals to all curious scientists for whom continuum mechanics as a vividly evolving science still has its own mysteries.

Creep Problems in Structural Members

Author : I︠U︡riĭ Nikolaevich Rabotnov
Publisher :
ISBN 13 :
Total Pages : 854 pages
Book Rating : 4.:/5 (89 download)

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Book Synopsis Creep Problems in Structural Members by : I︠U︡riĭ Nikolaevich Rabotnov

Download or read book Creep Problems in Structural Members written by I︠U︡riĭ Nikolaevich Rabotnov and published by . This book was released on 1969 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt:

New Trends in Nanotechnology and Fractional Calculus Applications

Author : Dumitru Baleanu
Publisher : Springer Science & Business Media
ISBN 13 : 9048132932
Total Pages : 518 pages
Book Rating : 4.0/5 (481 download)

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Book Synopsis New Trends in Nanotechnology and Fractional Calculus Applications by : Dumitru Baleanu

Download or read book New Trends in Nanotechnology and Fractional Calculus Applications written by Dumitru Baleanu and published by Springer Science & Business Media. This book was released on 2010-03-14 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years fractional calculus has played an important role in various fields such as mechanics, electricity, chemistry, biology, economics, modeling, identification, control theory and signal processing. The scope of this book is to present the state of the art in the study of fractional systems and the application of fractional differentiation. Furthermore, the manufacture of nanowires is important for the design of nanosensors and the development of high-yield thin films is vital in procuring clean solar energy. This wide range of applications is of interest to engineers, physicists and mathematicians.

Mittag-Leffler Functions, Related Topics and Applications

Author : Rudolf Gorenflo
Publisher : Springer
ISBN 13 : 3662439301
Total Pages : 454 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Mittag-Leffler Functions, Related Topics and Applications by : Rudolf Gorenflo

Download or read book Mittag-Leffler Functions, Related Topics and Applications written by Rudolf Gorenflo and published by Springer. This book was released on 2014-10-16 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a result of researchers’ and scientists’ increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have recently caught the interest of the scientific community. Focusing on the theory of the Mittag-Leffler functions, the present volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to the applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular the Mittag-Leffler functions allow us to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and its successors. The book is intended for a broad audience, comprising graduate students, university instructors and scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, theory of control and several other related areas.

Nonlocal and Fractional Operators

Author : Luisa Beghin
Publisher : Springer Nature
ISBN 13 : 3030692361
Total Pages : 308 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Nonlocal and Fractional Operators by : Luisa Beghin

Download or read book Nonlocal and Fractional Operators written by Luisa Beghin and published by Springer Nature. This book was released on 2021-07-23 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this volume is to explore new bridges between different research areas involved in the theory and applications of the fractional calculus. In particular, it collects scientific and original contributions to the development of the theory of nonlocal and fractional operators. Special attention is given to the applications in mathematical physics, as well as in probability. Numerical methods aimed to the solution of problems with fractional differential equations are also treated in the book. The contributions have been presented during the international workshop "Nonlocal and Fractional Operators", held in Sapienza University of Rome, in April 2019, and dedicated to the retirement of Prof. Renato Spigler (University Roma Tre). Therefore we also wish to dedicate this volume to this occasion, in order to celebrate his scientific contributions in the field of numerical analysis and fractional calculus. The book is suitable for mathematicians, physicists and applied scientists interested in the various aspects of fractional calculus.

Viscoelastic Solids (1998)

Author : Roderic S. Lakes
Publisher : CRC Press
ISBN 13 : 1351355643
Total Pages : 476 pages
Book Rating : 4.3/5 (513 download)

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Book Synopsis Viscoelastic Solids (1998) by : Roderic S. Lakes

Download or read book Viscoelastic Solids (1998) written by Roderic S. Lakes and published by CRC Press. This book was released on 2017-11-22 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Viscoelastic Solids covers the mathematical theory of viscoelasticity and physical insights, causal mechanisms, and practical applications. The book: presents a development of the theory, addressing both transient and dynamic aspects as well as emphasizing linear viscoelasticity synthesizes the structure of the theory with the aim of developing physical insight illustrates the methods for the solution of stress analysis problems in viscoelastic objects explores experimental methods for the characterization of viscoelastic materials describes the phenomenology of viscoelasticity in a variety of materials, including polymers, metals, high damping alloys, rock, piezoelectric materials, cellular solids, dense composite materials, and biological materials analyzes high damping and extremely low damping provides the theory of viscoelastic composite materials, including examples of various types of structure and the relationships between structure and mechanical properties contains examples on the use of viscoelastic materials in preventing and alleviating human suffering Viscoelastic Solids also demonstrates the use of viscoelasticity for diverse applications, such as earplugs, gaskets, computer disks, satellite stability, medical diagnosis, injury prevention, vibration abatement, tire performance, sports, spacecraft explosions, and music.

The Variable-Order Fractional Calculus of Variations

Author : Ricardo Almeida
Publisher : Springer
ISBN 13 : 3319940066
Total Pages : 135 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis The Variable-Order Fractional Calculus of Variations by : Ricardo Almeida

Download or read book The Variable-Order Fractional Calculus of Variations written by Ricardo Almeida and published by Springer. This book was released on 2018-06-29 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Variable-Order Fractional Calculus of Variations is devoted to the study of fractional operators with variable order and, in particular, variational problems involving variable-order operators. This brief presents a new numerical tool for the solution of differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one, an approximation formula is obtained in terms of standard (integer-order) derivatives only. Estimations for the error of the approximations are also provided. The contributors consider variational problems that may be subject to one or more constraints, where the functional depends on a combined Caputo derivative of variable fractional order. In particular, they establish necessary optimality conditions of Euler–Lagrange type. As the terminal point in the cost integral is free, as is the terminal state, transversality conditions are also obtained. The Variable-Order Fractional Calculus of Variations is a valuable source of information for researchers in mathematics, physics, engineering, control and optimization; it provides both analytical and numerical methods to deal with variational problems. It is also of interest to academics and postgraduates in these fields, as it solves multiple variational problems subject to one or more constraints in a single brief.

Applications Of Fractional Calculus In Physics

Author : Rudolf Hilfer
Publisher : World Scientific
ISBN 13 : 9814496200
Total Pages : 473 pages
Book Rating : 4.8/5 (144 download)

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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.