Bogoljub Stankovic's Books

Fractional Calculus with Applications in Mechanics

Vibrations and Diffusion Processes

By: Teodor M. Atanackovic,Stevan Pilipovic,Bogoljub Stankovic,Dusan Zorica

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Fractional Calculus with Applications in Mechanics

Vibrations and Diffusion Processes

By: Teodor M. Atanackovic,Stevan Pilipovic,Bogoljub Stankovic,Dusan Zorica

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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Page Count

306

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118577469

ISBN 13

9781118577462

Asymptotic Behavior of Generalized Functions

By: Stevan Pilipovic,Bogoljub Stankovic,Jasson Vindas

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Asymptotic Behavior of Generalized Functions

By: Stevan Pilipovic,Bogoljub Stankovic,Jasson Vindas

The asymptotic analysis has obtained new impulses with the general development of various branches of mathematical analysis and their applications. In this book, such impulses originate from the use of slowly varying functions and the asymptotic behavior of generalized functions. The most developed approaches related to generalized functions are those of Vladimirov, Drozhinov and Zavyalov, and that of Kanwal and Estrada. The first approach is followed by the authors of this book and extended in the direction of the S-asymptotics. The second approach OCo of Estrada, Kanwal and Vindas OCo is related to moment asymptotic expansions of generalized functions and the Ces''aro behavior. The main features of this book are the uses of strong methods of functional analysis and applications to the analysis of asymptotic behavior of solutions to partial differential equations, Abelian and Tauberian type theorems for integral transforms as well as for the summability of Fourier series and integrals. The book can be used by applied mathematicians, physicists, engineers and others who use classical asymptotic methods and wish to consider non-classical objects (generalized functions) and their asymptotics now in a more advanced setting.

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Page Count

309

Publisher

World Scientific

Published Date

ISBN 10

9814366854

ISBN 13

9789814366854

Fractional Calculus with Applications in Mechanics

Wave Propagation, Impact and Variational Principles

By: Teodor M. Atanackovic,Stevan Pilipovic,Bogoljub Stankovic,Dusan Zorica

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Fractional Calculus with Applications in Mechanics

Wave Propagation, Impact and Variational Principles

By: Teodor M. Atanackovic,Stevan Pilipovic,Bogoljub Stankovic,Dusan Zorica

The books Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes and Fractional Calculus with Applications in Mechanics: Wave Propagation, Impact and Variational Principles contain various applications of fractional calculus to the fields of classical mechanics. Namely, the books study problems in fields such as viscoelasticity of fractional order, lateral vibrations of a rod of fractional order type, lateral vibrations of a rod positioned on fractional order viscoelastic foundations, diffusion-wave phenomena, heat conduction, wave propagation, forced oscillations of a body attached to a rod, impact and variational principles of a Hamiltonian type. The books will be useful for graduate students in mechanics and applied mathematics, as well as for researchers in these fields. Part 1 of this book presents an introduction to fractional calculus. Chapter 1 briefly gives definitions and notions that are needed later in the book and Chapter 2 presents definitions and some of the properties of fractional integrals and derivatives. Part 2 is the central part of the book. Chapter 3 presents the analysis of waves in fractional viscoelastic materials in infinite and finite spatial domains. In Chapter 4, the problem of oscillations of a translatory moving rigid body, attached to a heavy, or light viscoelastic rod of fractional order type, is studied in detail. In Chapter 5, the authors analyze a specific engineering problem of the impact of a viscoelastic rod against a rigid wall. Finally, in Chapter 6, some results for the optimization of a functional containing fractional derivatives of constant and variable order are presented.

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Page Count

437

Publisher

John Wiley & Sons

Published Date

ISBN 10

1118909135

ISBN 13

9781118909133

Fractional Calculus with Applications in Mechanics

Wave Propagation, Impact and Variational Principles

By: Teodor M. Atanackovic,Stevan Pilipovic,Bogoljub Stankovic,Dusan Zorica

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Fractional Calculus with Applications in Mechanics

Wave Propagation, Impact and Variational Principles

By: Teodor M. Atanackovic,Stevan Pilipovic,Bogoljub Stankovic,Dusan Zorica

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Solve jigsaw puzzle

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Page Count

437

Publisher

John Wiley & Sons

Published Date

ISBN 10

1848216793

ISBN 13

9781848216792

Asymptotic Behavior of Generalized Functions

By: Stevan Pilipovi?,Bogoljub Stankovi?,Jasson Vindas

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Asymptotic Behavior of Generalized Functions

By: Stevan Pilipovi?,Bogoljub Stankovi?,Jasson Vindas

The asymptotic analysis has obtained new impulses with the general development of various branches of mathematical analysis and their applications. In this book, such impulses originate from the use of slowly varying functions and the asymptotic behavior of generalized functions. The most developed approaches related to generalized functions are those of Vladimirov, Drozhinov and Zavyalov, and that of Kanwal and Estrada. The first approach is followed by the authors of this book and extended in the direction of the S-asymptotics. The second approach ? of Estrada, Kanwal and Vindas ? is related to moment asymptotic expansions of generalized functions and the Ces'aro behavior. The main features of this book are the uses of strong methods of functional analysis and applications to the analysis of asymptotic behavior of solutions to partial differential equations, Abelian and Tauberian type theorems for integral transforms as well as for the summability of Fourier series and integrals. The book can be used by applied mathematicians, physicists, engineers and others who use classical asymptotic methods and wish to consider non-classical objects (generalized functions) and their asymptotics now in a more advanced setting.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

309

Publisher

World Scientific

Published Date

ISBN 10

9814366846

ISBN 13

9789814366847

Book's by Bogoljub Stankovic

Fractional Calculus with Applications in Mechanics

Fractional Calculus with Applications in Mechanics

Asymptotic Behavior of Generalized Functions

Asymptotic Behavior of Generalized Functions

Fractional Calculus with Applications in Mechanics

Fractional Calculus with Applications in Mechanics

Fractional Calculus with Applications in Mechanics

Fractional Calculus with Applications in Mechanics

Asymptotic Behavior of Generalized Functions

Asymptotic Behavior of Generalized Functions

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