Fractional Calculus And Waves In Linear Viscoelasticity An Introduction To Mathematical Models
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| Author | : Francesco Mainardi |
| Publisher | : World Scientific |
| Total Pages | : 626 |
| Release | : 2022-08-16 |
| Genre | : Mathematics |
| ISBN | : 1783264004 |
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.
| Author | : Jagdev Singh |
| Publisher | : Springer Nature |
| Total Pages | : 433 |
| Release | : 2021-08-26 |
| Genre | : Technology & Engineering |
| ISBN | : 3030771695 |
This book contains several contemporary topics in the areas of mathematical modelling and computation for complex systems. The readers find several new mathematical methods, mathematical models and computational techniques having significant relevance in studying various complex systems. The chapters aim to enrich the understanding of topics presented by carefully discussing the associated problems and issues, possible solutions and their applications or relevance in other scientific areas of study and research. The book is a valuable resource for graduate students, researchers and educators in understanding and studying various new aspects associated with complex systems. Key Feature • The chapters include theory and application in a mix and balanced way. • Readers find reasonable details of developments concerning a topic included in this book. • The text is emphasized to present in self-contained manner with inclusion of new research problems and questions.
| Author | : George A. Anastassiou |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 494 |
| Release | : 2014-07-08 |
| Genre | : Mathematics |
| ISBN | : 1461463939 |
Advances in Applied Mathematics and Approximation Theory: Contributions from AMAT 2012 is a collection of the best articles presented at “Applied Mathematics and Approximation Theory 2012,” an international conference held in Ankara, Turkey, May 17-20, 2012. This volume brings together key work from authors in the field covering topics such as ODEs, PDEs, difference equations, applied analysis, computational analysis, signal theory, positive operators, statistical approximation, fuzzy approximation, fractional analysis, semigroups, inequalities, special functions and summability. The collection will be a useful resource for researchers in applied mathematics, engineering and statistics.
| Author | : Aliaa Burqan |
| Publisher | : Springer Nature |
| Total Pages | : 594 |
| Release | : |
| Genre | : |
| ISBN | : 9819748763 |
| Author | : Valentin Afraimovich |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 297 |
| Release | : 2013-11-22 |
| Genre | : Technology & Engineering |
| ISBN | : 3319023535 |
This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.
| Author | : Kai Diethelm |
| Publisher | : Springer |
| Total Pages | : 251 |
| Release | : 2010-08-18 |
| Genre | : Mathematics |
| ISBN | : 3642145744 |
Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.
| Author | : Mauro Fabrizio |
| Publisher | : SIAM |
| Total Pages | : 210 |
| Release | : 1992-01-01 |
| Genre | : Science |
| ISBN | : 0898712661 |
Describes general mathematical modeling of viscoelastic materials as systems with fading memory. Discusses the interrelation between topics such as existence, uniqueness, and stability of initial boundary value problems, variational and extremum principles, and wave propagation. Demonstrates the deep connection between the properties of the solution to initial boundary value problems and the requirements of the general physical principles. Discusses special techniques and new methods, including Fourier and Laplace transforms, extremum principles via weight functions, and singular surfaces and discontinuity waves.
| Author | : Yuriy Povstenko |
| Publisher | : Springer Nature |
| Total Pages | : 457 |
| Release | : |
| Genre | : |
| ISBN | : 3031645871 |
| Author | : Dumitru Baleanu |
| Publisher | : World Scientific |
| Total Pages | : 426 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 9814355208 |
This title will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods.
| Author | : Anatoly Kochubei |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 528 |
| Release | : 2019-02-19 |
| Genre | : Mathematics |
| ISBN | : 3110571668 |
This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.
