Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes
Copyright © 2014 John Wiley & Sons, Inc.
Author(s): Teodor M. Atanacković, Stevan Pilipović, Bogoljub Stanković, Dušan Zorica
Published Online: 21 FEB 2014
Print ISBN: 9781848214170
Online ISBN: 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.