Fractional Calculus with Applications in Mechanics
Vibrations and Diffusion Processes
1st Edition
Published on 28. January 2014
Book
Hardback
336 pages
978-1-84821-417-0 (ISBN)
Description
This book contains mathematical preliminaries in which basic definitions of fractional derivatives and spaces are presented. The central part of the book contains various applications in classical mechanics including fields such as: viscoelasticity, heat conduction, wave propagation and variational Hamilton-type principles. Mathematical rigor will be observed in the applications. The authors provide some problems formulated in the classical setting and some in the distributional setting. The solutions to these problems are presented in analytical form and these solutions are then analyzed numerically. Theorems on the existence of solutions will be presented for all examples discussed. In using various constitutive equations the restrictions following from the second law of thermodynamics will be implemented. Finally, the physical implications of obtained solutions will be discussed in detail.
Reviews / Votes
"The book will be useful to researchers and students looking for applications of fractional calculus in applied mechanics and engineering." (Zentralblatt MATH, 1 November 2014)More details
Language
English
Place of publication
London
United Kingdom
Target group
Professional and scholarly
Dimensions
Height: 241 mm
Width: 163 mm
Thickness: 25 mm
Weight
640 gr
ISBN-13
978-1-84821-417-0 (9781848214170)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Teodor M. Atanackovic | Stevan Pilipovic | Bogoljub Stankovic
Fractional Calculus with Applications in Mechanics
Vibrations and Diffusion Processes
E-Book
02/2014
Wiley-ISTE
€160.99
Available for download
Teodor M. Atanackovic | Stevan Pilipovic | Bogoljub Stankovic
Fractional Calculus with Applications in Mechanics
Vibrations and Diffusion Processes
E-Book
02/2014
Wiley-ISTE
€160.99
Available for download
Persons
Teodor M. Atanackovic is Full Professor at the University of Novi Sad, Serbia. He has authored or co-authored 8 books and more than 170 articles for journals and proceedings.
Stevan Pilipovic is Full Professor at the University of Novi Sad, Serbia. He has written more than 180 scientific papers in refereed international journals, and more than 35 contributions to special volumes and international conference proceedings.
Bogoljub Stankovic is a retired Professor at the University of Novi Sad, Serbia. His interests include classical theory of integral transforms and operational calculus, special functions, functional analysis, generalized functions and hyperfunctions. He has authored several books and more than 200 articles for journals and proceedings.
Dusan Zorica is Assistant Research Professor at the Mathematical Institute, Serbian Academy of Arts and Sciences in Belgrade, Serbia. He has authored or co-authored over 30 journal and conference papers. His current research interest is in various aspects of fractional calculus and its application to physical problems.
Stevan Pilipovic is Full Professor at the University of Novi Sad, Serbia. He has written more than 180 scientific papers in refereed international journals, and more than 35 contributions to special volumes and international conference proceedings.
Bogoljub Stankovic is a retired Professor at the University of Novi Sad, Serbia. His interests include classical theory of integral transforms and operational calculus, special functions, functional analysis, generalized functions and hyperfunctions. He has authored several books and more than 200 articles for journals and proceedings.
Dusan Zorica is Assistant Research Professor at the Mathematical Institute, Serbian Academy of Arts and Sciences in Belgrade, Serbia. He has authored or co-authored over 30 journal and conference papers. His current research interest is in various aspects of fractional calculus and its application to physical problems.
Content
Preface ix
Part 1. Mathematical Preliminaries, Definitions and Properties of Fractional Integrals and Derivatives 1
Chapter 1. Mathematical Preliminaries 3
Chapter 2. Basic Definitions and Properties of Fractional Integrals and Derivatives 17
Part 2. Mechanical Systems 49
Chapter 3. Restrictions Following from the Thermodynamics for Fractional Derivative Models of a Viscoelastic Body 51
Chapter 4. Vibrations with Fractional Dissipation 83
Chapter 5. Lateral Vibrations and Stability of Viscoelastic Rods 123
Chapter 6. Fractional Diffusion-Wave Equations 185
Chapter 7. Fractional Heat Conduction Equations 257
Bibliography 289
Index 311
Part 1. Mathematical Preliminaries, Definitions and Properties of Fractional Integrals and Derivatives 1
Chapter 1. Mathematical Preliminaries 3
Chapter 2. Basic Definitions and Properties of Fractional Integrals and Derivatives 17
Part 2. Mechanical Systems 49
Chapter 3. Restrictions Following from the Thermodynamics for Fractional Derivative Models of a Viscoelastic Body 51
Chapter 4. Vibrations with Fractional Dissipation 83
Chapter 5. Lateral Vibrations and Stability of Viscoelastic Rods 123
Chapter 6. Fractional Diffusion-Wave Equations 185
Chapter 7. Fractional Heat Conduction Equations 257
Bibliography 289
Index 311