Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes

Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes

Author(s): Teodor M. Atanacković, Stevan Pilipović, Bogoljub Stanković, Dušan Zorica

Published Online: 21 FEB 2014

Print ISBN: 9781848214170

Online ISBN: 9781118577530

DOI: 10.1002/9781118577530

Series Editor(s): Noël Challamel

About this Book

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.

Table of contents

    1. You have free access to this content
  1. Part 1: Mathematical Preliminaries, Definitions and Properties of Fractional Integrals and Derivatives

    1. Chapter 1

      Mathematical Preliminaries (pages 1–16)

      Teodor M. Atanacković, Stevan Pilipović, Bogoljub Stanković and Dušan Zorica

    1. Chapter 2

      Basic Definitions and Properties of Fractional Integrals and Derivatives (pages 17–47)

      Teodor M. Atanacković, Stevan Pilipović, Bogoljub Stanković and Dušan Zorica

  2. Part 2: Mechanical Systems

    1. Chapter 4

      Vibrations with Fractional Dissipation (pages 83–122)

      Teodor M. Atanacković, Stevan Pilipović, Bogoljub Stanković and Dušan Zorica

    1. Chapter 5

      Lateral Vibrations and Stability of Viscoelastic Rods (pages 123–184)

      Teodor M. Atanacković, Stevan Pilipović, Bogoljub Stanković and Dušan Zorica

    1. Chapter 6

      Fractional Diffusion-Wave Equations (pages 185–255)

      Teodor M. Atanacković, Stevan Pilipović, Bogoljub Stanković and Dušan Zorica

    1. Chapter 7

      Fractional Heat Conduction Equations (pages 257–287)

      Teodor M. Atanacković, Stevan Pilipović, Bogoljub Stanković and Dušan Zorica

    1. You have free access to this content
    1. You have free access to this content

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