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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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Autore: Malinowska Agnieszka B Visualizza persona
Titolo: Advanced methods in the fractional calculus of variations [[electronic resource] /] / by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres Visualizza cluster
Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
Edizione: 1st ed. 2015.
Descrizione fisica: 1 online resource (142 p.)
Disciplina: 003.3
Soggetto topico: Calculus of variations
Control engineering
Economic theory
Mathematical models
System theory
Calculus of Variations and Optimal Control; Optimization
Control and Systems Theory
Mathematical Methods in Physics
Economic Theory/Quantitative Economics/Mathematical Methods
Mathematical Modeling and Industrial Mathematics
Systems Theory, Control
Persona (resp. second.): OdzijewiczTatiana
TorresDelfim F.M
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: 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.
Sommario/riassunto: 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.
Titolo autorizzato: Advanced Methods in the Fractional Calculus of Variations  Visualizza cluster
ISBN: 3-319-14756-0
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910299767303321
Lo trovi qui: Univ. Federico II
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Serie: SpringerBriefs in Applied Sciences and Technology, . 2191-530X