Advanced Methods in the Fractional Calculus of Variations
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Beschreibung
This brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the Euler–Lagrange equations to include fractional derivatives.
The dependence of Lagrangians on generalized fractional operators as well as on classical derivatives is considered along with still more general problems in which integer-order integrals are replaced by fractional integrals. General theorems are obtained for several types of variational problems for which recent results developed in the literature can be obtained as special cases. In particular, the authors offer necessary optimality conditions of Euler–Lagrange type for the fundamental and isoperimetric problems, transversality conditions, and Noether symmetry theorems. The existence of solutions is demonstrated under Tonelli type conditions. The results are used to prove the existence of eigenvalues and corresponding orthogonal eigenfunctions of fractional Sturm–Liouville problems.
Advanced Methods in the Fractional Calculus of Variations is a self-contained text which will be useful for graduate students wishing to learn about fractional-order systems. The detailed explanations will interest researchers with backgrounds in applied mathematics, control and optimization as well as in certain areas of physics and engineering.
Provides the reader with a unifying approach to the fractional calculus of variations The first treatment of the fractional calculus of variations and optimal control with general kernels Broadens accessibility of a recent and very active research area to a wider community Describes many open problems and challenges to motivate the work of other control theorists Includes supplementary material: sn.pub/extras
Autor*in
Agnieszka B. Malinowska
Themen in »Advanced Methods in the Fractional Calculus of Variations«
Calculus of Variations Direct Methods in Calculus of Variations Fractional Calculus of Variations Fractional Operators with Kernels Fractional Sturm–Liouville Problem Lagrange Type Necessary Optimality Conditions of Euler–Lagrange Type Noether’s Theorem Optimal Control
Stimmen zu »Advanced Methods in the Fractional Calculus of Variations«
“The authors study variational problems containing generalized fractional integrals and derivatives, following Euler-Lagrange type methods and also the direct methods of Tonelli and others. … Each chapter has its own reference list, which adds-up to a generous bibliography. The book will be attractive to graduate students wishing to enter this research area, as well as to researchers interested in control theory, optimization and other applications.” (Ubiratan D’Ambrosio, zbMATH 1330.49001, 2016)
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