Fractional Calculus with Applications in Mechanics

Vibrations and Diffusion Processes

Nonfiction, Science & Nature, Mathematics, Applied
Cover of the book Fractional Calculus with Applications in Mechanics by Bogoljub Stankovic, Teodor M. Atanackovic, Stevan Pilipovic, Dusan Zorica, Wiley
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Author: Bogoljub Stankovic, Teodor M. Atanackovic, Stevan Pilipovic, Dusan Zorica ISBN: 9781118577462
Publisher: Wiley Publication: February 19, 2014
Imprint: Wiley-ISTE Language: English
Author: Bogoljub Stankovic, Teodor M. Atanackovic, Stevan Pilipovic, Dusan Zorica
ISBN: 9781118577462
Publisher: Wiley
Publication: February 19, 2014
Imprint: Wiley-ISTE
Language: English

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.

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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.

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