Fractional calculus and waves in linear viscoelasticity : an introduction to mathematical models
著者
書誌事項
Fractional calculus and waves in linear viscoelasticity : an introduction to mathematical models
World Scientific, c2022
2nd ed
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
Fractional Calculus and Waves in Linear Viscoelasticity (Second Edition) is a self-contained treatment of the mathematical theory of linear (uni-axial) viscoelasticity (constitutive equation and waves) with particular regard to models based on fractional calculus. It serves as a general introduction to the above-mentioned areas of mathematical modeling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature. In particular the relevant role played by some special functions is pointed out along with their visualization through plots. Graphics are extensively used in the book and a large general bibliography is included at the end.This new edition keeps the structure of the first edition but each chapter has been revised and expanded, and new additions include a novel appendix on complete monotonic and Bernstein functions that are known to play a fundamental role in linear viscoelasticity.This book is suitable for engineers, graduate students and researchers interested in fractional calculus and continuum mechanics.
目次
- Essentials of Fractional Calculus
- Essentials of Linear Viscoelasticity
- Fractional Viscoelastic models
- Waves in Linear Viscoelastic Media: Dispersion and Dissipation
- Waves in Linear Viscoelastic Media: Asymptotic Representations
- Diffusion and Wave-Propagation via Fractional Calculus
- Appendices: The Eulerian Functions
- The Bessel Functions
- The Error Functions
- The Exponential Integral Functions
- The Mittag - Leffler Functions
- The Wright Functions.
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