Fractional calculus and waves in linear viscoelasticity : an introduction to mathematical models
This monograph provides a comprehensive overview of the author's work on the fields of fractional calculus and waves in linear viscoelastic media, which includes his pioneering contributions on the applications of special functions of the Mittag-Leffler and Wright types.It is intended to serve...
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| Main Author | |
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| Format | eBook Book |
| Language | English |
| Published |
London
Imperial College Press
2010
World Scientific Publishing Company IMPERIAL COLLEGE PRESS World Scientific Publishing |
| Subjects | |
| Online Access | Get full text |
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| Abstract | This monograph provides a comprehensive overview of the author's work on the fields of fractional calculus and waves in linear viscoelastic media, which includes his pioneering contributions on the applications of special functions of the Mittag-Leffler and Wright types.It is intended to serve 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 given in the huge general bibliography.This book is likely to be of interest to applied scientists and engineers. |
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| AbstractList | This monograph provides a comprehensive overview of the author's work on the fields of fractional calculus and waves in linear viscoelastic media, which includes his pioneering contributions on the applications of special functions of the Mittag-Leffler and Wright types.It is intended to serve 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 given in the huge general bibliography.This book is likely to be of interest to applied scientists and engineers. This monograph provides a comprehensive overview of the author's work on the fields of fractional calculus and waves in linear viscoelastic media, which includes his pioneering contributions on the applications of special functions of the Mittag-Leffler and Wright types.It is intended to serve 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 given in the huge general bibliography.This book is likely to be of interest to applied scientists and engineers.Sample Chapter(s)Chapter 1: Essentials of Fractional Calculus (376 KB)Contents:Essentials of Fractional CalculusEssentials of Linear ViscoelasticityFractional Viscoelastic ModelsWaves in Linear Viscoelastic Media: Dispersion and DissipationWaves in Linear Viscoelastic Media: Asymptotic RepresentationsDiffusion and Wave-Propagation via Fractional CalculusAppendices:The Eulerian FunctionsThe Bessel FunctionsThe Error FunctionsThe Exponential Integral FunctionsThe Mittag-Leffler FunctionsThe Wright FunctionsReadership: Graduate and PhD students in applied mathematics, classical physics, mechanical engineering and chemical physics; academic institutions; research centers. |
| Author | Mainardi, F. (Francesco) |
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| Keywords | Wright Functions Mittag-Leffler Functions Fractional Integrals Laplace Transforms Fractional Derivatives Waves Dispersion Fractional Calculus Fourier Transforms Anomalous Diffusion Linear Viscoelasticity Special Functions Dissipation Diffusion Rheological Models Integral Transforms |
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| Notes | Includes bibliographical references (p. 261-341) and index |
| PageCount | 1 online resource (368 pages) |
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| SubjectTerms | Applied Mathematics Fractional calculus Mathematical Physics MATHEMATICS Theoretical Physics Viscoelasticity Viscoelasticity -- Mathematical models Waves Waves -- Mathematical models |
| Title | Fractional calculus and waves in linear viscoelasticity : an introduction to mathematical models |
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