Francesco Mainardi 
FRAC CALC & WAVE LNR (2ND REV ED) 
An Introduction to Mathematical Models

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.

Contents:

• Preface to the Second Edition


• Preface to the First Edition


• Acknowledgments


• List of Figures


• List of Tables


• 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 Waves via Time Fractional Calculus


• Diffusion and Waves via Space–Time Fractional Calculus


• Appendices:
  
  
  
  • The Eulerian Functions
  
  
  • The Bessel Functions
  
  
  • The Error Functions
  
  
  • The Exponential Integral Functions
  
  
  • The Mittag-Leffler Functions
  
  
  • The Wright Functions
  
  
  • Complete Monotone and Bernstein Functions
  
  


• Bibliography


• Index

Readership: Engineers, graduate students and researchers in applied mathematics, physics and engineering departments.

‘The book is essential if one wishes to initiate research in the field of fractional rheology. The topic is quite promisimg and this book is a useful tool for taking the first step. In my opinion, it is well written and is very readable, with many technical details.’ – Dr José M Carcione Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS)

Key Features:

• Includes more details on the basic theory of linear viscoelasticity and in particular on the fractional models, with respect to the First Edition


• Provides details on the special functions of the Mittag-Leffler and Wright type


• Expands on the problems of fractional diffusion and fractional wave propagation


• Minimises use of mathematical formalities, treating mathematics as a type of language for everyday use rather than a body of theorems and proofs


• Emphasizes problems and solutions rather than theorems and their proofs