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Advanced Methods in the Fractional Calculus of Variations [electronic resource] / by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres.

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dc.contributor.author Malinowska, Agnieszka B. author.
dc.contributor.author Odzijewicz, Tatiana. author.
dc.contributor.author Torres, Delfim F.M. author.
dc.contributor.author SpringerLink (Online service)
dc.date.accessioned 2017-11-30T20:41:46Z
dc.date.available 2017-11-30T20:41:46Z
dc.date.created 2015.
dc.date.issued 2015
dc.identifier.isbn 9783319147567
dc.identifier.uri http://dspace.conacyt.gov.py/xmlui/handle/123456789/12788
dc.description XII, 135 p.
dc.description.abstract 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.
dc.description.tableofcontents 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.
dc.language eng
dc.publisher Cham : Springer International Publishing : Imprint: Springer, 2015.
dc.relation.ispartofseries Springer eBooks
dc.relation.ispartofseries SpringerBriefs in Applied Sciences and Technology, 2191-530X
dc.relation.ispartofseries SpringerBriefs in Applied Sciences and Technology, 2191-530X
dc.relation.uri http://cicco.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-14756-7
dc.subject Mathematics.
dc.subject System theory.
dc.subject Mathematical models.
dc.subject Calculus of variations.
dc.subject Physics.
dc.subject Control engineering.
dc.subject Economic theory.
dc.subject Mathematics.
dc.subject Calculus of Variations and Optimal Control; Optimization.
dc.subject Control.
dc.subject Mathematical Methods in Physics.
dc.subject Economic Theory/Quantitative Economics/Mathematical Methods.
dc.subject Mathematical Modeling and Industrial Mathematics.
dc.subject Systems Theory, Control.
dc.subject.ddc 515.64 23
dc.subject.lcc QA315-316
dc.subject.lcc QA402.3
dc.subject.lcc QA402.5-QA402.6
dc.subject.other Mathematics and Statistics (Springer-11649)
dc.title Advanced Methods in the Fractional Calculus of Variations [electronic resource] / by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres.
dc.type text
dc.identifier.doi 10.1007/978-3-319-14756-7
dc.identifier.bib 978-3-319-14756-7
dc.format.rdamedia computer
dc.format.rdacarrier online resource
dc.format.rda text file PDF


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