Fractional Calculus with Applications in Mechanics – Vibrations and Diffusion Processes
Vibrations and Diffusion Processes
Samenvatting
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.
Specificaties
Inhoudsopgave
<p>Chapter 1. Mathematical Preliminaries 3<br /><br />Chapter 2. Basic Definitions and Properties of Fractional Integrals and Derivatives 17</p>
<p>Part 2. Mechanical Systems 49</p>
<p>Chapter 3. Restrictions Following from the Thermodynamics for Fractional Derivative Models of a Viscoelastic Body 51</p>
<p>Chapter 4. Vibrations with Fractional Dissipation 83</p>
<p>Chapter 5. Lateral Vibrations and Stability of Viscoelastic Rods 123</p>
<p>Chapter 6. Fractional Diffusion–Wave Equations 185</p>
<p>Chapter 7. Fractional Heat Conduction Equations 257<br /><br />Bibliography 289<br /><br />Index 311</p>