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Fractional Calculus with Applications in Mechanics

Vibrations and Diffusion Processes

Teodor M. Atanackovic, University of Novi Sad, Serbia Stevan Pilipovic, University of Novi Sad, Serbia Bogoljub Stankovic, University of Novi Sad, Serbia Dusan Zorica, Mathematical Institute, Serbian Academy of Arts and Sciences in Belgrade, Serbia

ISBN: 9781848214170

Publication Date: January 2014   Hardback   336 pp.

170.00 USD


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Description

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.

Contents

Part 1. Mathematical Preliminaries, Definitions and Properties of Fractional Integrals and Derivatives
1. Mathematical Preliminaries.
2. Basic Definitions and Properties of Fractional Integrals and Derivatives.
Part 2. Mechanical Systems
3. Restrictions Following from the Thermodynamics for Fractional Derivative Models of a Viscoelastic Body.
4. Vibrations with Fractional Dissipation.
5. Lateral Vibrations and Stability of Viscoelastic Rods.
6. Fractional Diffusion-Wave Equations.
7. Fractional Heat Conduction Equations.

About the Authors

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.

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