Fractional calculus with applications in mechanics : vibrations and diffusion processes
- Atanacković, Teodor M., 1945- author.
- London ; Hoboken, NJ : ISTE : John Wiley & Sons, Inc., 2014.
- Physical description
- xiii, 315 pages : ill. ; 24 cm.
- Mechanical engineering and solid mechanics series.
QA314 .A83 2014
- Unknown QA314 .A83 2014
- Includes bibliographical references (pages 289-310) and index.
- 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.
- (source: Nielsen Book Data)
- Publisher's Summary
- 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.
(source: Nielsen Book Data)
- Publication date
- Teodor M. Atanacković, Stevan Pilipović, Bogoljub Stanković, Dušan Zorica.
- Mechanical Engineering and Solid Mechanics Series
- 9781848214170 (hbk.)
- 1848214170 (hbk.)