Fractional Calculus with Applications in Mechanics
Vibrations and Diffusion Processes
Published on 19. February 2014
336 pages
978-1-118-57750-9 (ISBN)
Description
This book contains mathematical preliminaries in which basicdefinitions of fractional derivatives and spaces are presented. Thecentral part of the book contains various applications in classicalmechanics including fields such as: viscoelasticity, heatconduction, wave propagation and variational Hamilton-typeprinciples. Mathematical rigor will be observed in theapplications. The authors provide some problems formulated in theclassical setting and some in the distributional setting. Thesolutions to these problems are presented in analytical form andthese solutions are then analyzed numerically. Theorems on theexistence of solutions will be presented for all examplesdiscussed. In using various constitutive equations the restrictionsfollowing from the second law of thermodynamics will beimplemented. Finally, the physical implications of obtainedsolutions will be discussed in detail.
Reviews / Votes
"The book will be useful to researchers and studentslooking for applications of fractional calculus in appliedmechanics and engineering." (Zentralblatt MATH,1 November 2014)More details
Other editions
Additional editions
Teodor M. Atanackovic | Stevan Pilipovic | Bogoljub Stankovic
Fractional Calculus with Applications in Mechanics
Vibrations and Diffusion Processes
Book
01/2014
1st Edition
Wiley-ISTE
€235.04
Shipment within 15-20 days
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
