Introduction To The Fractional Calculus Of Variations
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A01=Agnieszka Barbara Malinowska
A01=Delfim F M Torres
Author_Agnieszka Barbara Malinowska
Author_Delfim F M Torres
Calculus of Variations
Caputo Operators
Category=PBKQ
DuBois-Reymond Conditions
DuBoisAcAEURA"Reymond Conditions
DuBois–Reymond Conditions
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Euler-Lagrange Equations
EulerAcAEURA"Lagrange Equations
Euler–Lagrange Equations
Fractional Calculus
Hamiltonian Formalism
Isoperimetric Problems
Mathematics
Mechanics
Noether's Theorem
Optimal Control
Physics
Riemann-Liouville Operators
RiemannAcAEURA"Liouville Operators
Riemann–Liouville Operators
Riesz-Caputo Derivatives
RieszAcAEURA"Caputo Derivatives
Riesz–Caputo Derivatives
Transversality Conditions
Product details
- ISBN 9781848169661
- Publication Date: 14 Nov 2012
- Publisher: Imperial College Press
- Publication City/Country: GB
- Product Form: Hardback
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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.
