TY  - BOOK
AU  - Malinowska,Agnieszka B.
AU  - Odzijewicz,Tatiana
AU  - Torres,Delfim F.M.
ED  - SpringerLink (Online service)
TI  - Advanced Methods in the Fractional Calculus of Variations
T2  - SpringerBriefs in Applied Sciences and Technology,
SN  - 9783319147567
AV  - QA315-316 
U1  - 515.64 23
PY  - 2015///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - mathematics
KW  - System theory
KW  - Mathematical models
KW  - Calculus of variations
KW  - physics
KW  - Control Engineering
KW  - economic theory
KW  - Mathematics
KW  - Calculus of Variations and Optimal Control; Optimization
KW  - control
KW  - Mathematical Methods in Physics
KW  - Economic Theory/Quantitative Economics/Mathematical Methods
KW  - Mathematical Modeling and Industrial Mathematics
KW  - Systems Theory, Control
N1  - 1. Introduction -- 2. Fractional Calculus -- 3. Fractional Calculus of Variations -- 4. Standard Methods in Fractional Variational Calculus -- 5. Direct Methods in Fractional Calculus of Variations -- 6. Application to the Sturm-Liouville Problem -- 7. Conclusion -- Appendix - Two Convergence Lemmas -- Index
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-319-14756-7
ER  -