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Advanced Methods in the Fractional Calculus of Variations
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 fractiona...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Springer,
2015.
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| Edición: | 1st ed. 2015. |
| Colección: | SpringerBriefs in Applied Sciences and Technology,
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| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
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| 001 | 978-3-319-14756-7 | ||
| 003 | DE-He213 | ||
| 005 | 20220119194838.0 | ||
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| 008 | 150205s2015 sz | s |||| 0|eng d | ||
| 020 | |a 9783319147567 |9 978-3-319-14756-7 | ||
| 024 | 7 | |a 10.1007/978-3-319-14756-7 |2 doi | |
| 050 | 4 | |a QA402.5-402.6 | |
| 050 | 4 | |a QA315-316 | |
| 072 | 7 | |a PBU |2 bicssc | |
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| 100 | 1 | |a Malinowska, Agnieszka B. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Advanced Methods in the Fractional Calculus of Variations |h [electronic resource] / |c by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres. |
| 250 | |a 1st ed. 2015. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2015. | |
| 300 | |a XII, 135 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a SpringerBriefs in Applied Sciences and Technology, |x 2191-5318 | |
| 505 | 0 | |a 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. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Mathematical optimization. | |
| 650 | 0 | |a Calculus of variations. | |
| 650 | 0 | |a Control engineering. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 0 | |a Econometrics. | |
| 650 | 0 | |a Mathematical models. | |
| 650 | 0 | |a System theory. | |
| 650 | 0 | |a Control theory. | |
| 650 | 1 | 4 | |a Calculus of Variations and Optimization. |
| 650 | 2 | 4 | |a Control and Systems Theory. |
| 650 | 2 | 4 | |a Mathematical Methods in Physics. |
| 650 | 2 | 4 | |a Quantitative Economics. |
| 650 | 2 | 4 | |a Mathematical Modeling and Industrial Mathematics. |
| 650 | 2 | 4 | |a Systems Theory, Control . |
| 700 | 1 | |a Odzijewicz, Tatiana. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Torres, Delfim F.M. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783319147574 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319147550 |
| 830 | 0 | |a SpringerBriefs in Applied Sciences and Technology, |x 2191-5318 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-319-14756-7 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||