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Advanced methods in the fractional c...

Malinowska, Agnieszka B.

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Advanced methods in the fractional calculus of variations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Advanced methods in the fractional calculus of variations/ by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres.
Author:	Malinowska, Agnieszka B.
other author:	Odzijewicz, Tatiana.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	xii, 135 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Fractional calculus. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-14756-7
ISBN:	9783319147567 (electronic bk.)

Advanced methods in the fractional calculus of variations
Malinowska, Agnieszka B.

Advanced methods in the fractional calculus of variations[electronic resource] /by Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres. - Cham :Springer International Publishing :2015. - xii, 135 p. :ill., digital ;24 cm. - SpringerBriefs in applied sciences and technology,2191-530X. - SpringerBriefs in applied sciences and technology..

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.

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.

ISBN: 9783319147567 (electronic bk.)

Standard No.: 10.1007/978-3-319-14756-7doiSubjects--Topical Terms:

898980
Fractional calculus.

LC Class. No.: QA314

Dewey Class. No.: 515.83

Advanced methods in the fractional calculus of variations
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100 1 $a Malinowska, Agnieszka B. $3 2012691
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.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xii, 135 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in applied sciences and technology, $x 2191-530X
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 Fractional calculus. $3 898980
650 0 $a Calculus of variations. $3 516604
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 898674
650 2 4 $a Control. $3 1006321
650 2 4 $a Mathematical Methods in Physics. $3 890898
650 2 4 $a Game Theory/Mathematical Methods. $3 892394
650 2 4 $a Mathematical Modeling and Industrial Mathematics. $3 891089
650 2 4 $a Systems Theory, Control. $3 893834
700 1 $a Odzijewicz, Tatiana. $3 2134868
700 1 $a Torres, Delfim F.M. $3 2056837
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in applied sciences and technology. $3 1565541
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-14756-7
950 $a Mathematics and Statistics (Springer-11649)