
Introduction To The Fractional Calculus Of Variations
Imperial College Press
Published on 14. November 2012
Book
Hardback
292 pages
978-1-84816-966-1 (ISBN)
Description
This invaluable book provides a broad introduction to the fascinating and beautiful subject of Fractional Calculus of Variations (FCV). In 1996, FVC evolved in order to better describe non-conservative systems in mechanics. The inclusion of non-conservatism is extremely important from the point of view of applications. Forces that do not store energy are always present in real systems. They remove energy from the systems and, as a consequence, Noether's conservation laws cease to be valid. However, it is still possible to obtain the validity of Noether's principle using FCV. The new theory provides a more realistic approach to physics, allowing us to consider non-conservative systems in a natural way. The authors prove the necessary Euler-Lagrange conditions and corresponding Noether theorems for several types of fractional variational problems, with and without constraints, using Lagrangian and Hamiltonian formalisms. Sufficient optimality conditions are also obtained under convexity, and Leitmann's direct method is discussed within the framework of FCV.The book is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and ambitious undergraduates in mathematics and mechanics. It provides an opportunity for an introduction to FCV for experienced researchers. The explanations in the book are detailed, in order to capture the interest of the curious reader, and the book provides the necessary background material required to go further into the subject and explore the rich research literature.
More details
Language
English
Place of publication
London
United Kingdom
Target group
College/higher education
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 20 mm
Weight
580 gr
ISBN-13
978-1-84816-966-1 (9781848169661)
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Schweitzer Classification
Persons
Author
Univ Of Aveiro, Portugal
Bialystok Univ Of Technology, Poland
Content
The Classical Calculus of Variations; Fractional Calculus of Variations via Riemann - Liouville Operators; Fractional Calculus of Variations via Caputo Operators; Other Approaches to the Fractional Calculus of Variations; Towards a Combined Fractional Mechanics and Quantization.