Fractional Calculus and Waves in Linear Viscoelasticity An Introduction to Mathematical Models, 2nd Edition

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 Descriptions. 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.
Contentsreface to the Second EditionPreface to the First EditionAcknowledgmentsList of FiguresList of TablesEssentials of Fractional CalculusEssentials of Linear ViscoelasticityFractional Viscoelastic ModelsWaves in Linear Viscoelastic Media: Dispersion and DissipationWaves in Linear Viscoelastic Media: Asymptotic RepresentationsDiffusion and Waves via Time Fractional CalculusDiffusion and Waves via Space-Time Fractional CalculusAppendices:The Eulerian FunctionsThe Bessel FunctionsThe Error FunctionsThe Exponential Integral FunctionsThe Mittag-Leffler FunctionsThe Wright FunctionsComplete Monotone and Bernstein FunctionsBibliographyIndex
Readership: Engineers, graduate students and researchers in applied mathematics, physics and engineering departments.

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