Atanackovic / Pilipovic / Stankovic Fractional Calculus with Applications in Mechanics

Vibrations and Diffusion Processes
1. Auflage 2014
ISBN: 978-1-118-57750-9
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 336 Seiten, E-Book

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.

Autoren/Hrsg.

Atanackovic, Teodor M.

Pilipovic, Stevan

Stankovic, Bogoljub

Zorica, Dusan

Inhaltsverzeichnis

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