國立高雄大學圖資館 |

Language: English

Back

Advanced methods in the fractional c...

Malinowska, Agnieszka B.

Advanced methods in the fractional calculus of variations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Advanced methods in the fractional calculus of variationsby 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.
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:

208302
Fractional calculus.

LC Class. No.: QA314

Dewey Class. No.: 515.83

Advanced methods in the fractional calculus of variations
LDR:02829nmm a2200349 a 4500 001 461948
003 DE-He213
005 20150922111739.0
006 m d
007 cr nn 008maaau
008 151110s2015 gw s 0 eng d
020 $a 9783319147567 (electronic bk.)
020 $a 9783319147550 (paper)
024 7 $a 10.1007/978-3-319-14756-7 $2 doi
035 $a 978-3-319-14756-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA314
072 7 $a PBKQ $2 bicssc
072 7 $a PBU $2 bicssc
072 7 $a MAT005000 $2 bisacsh
072 7 $a MAT029020 $2 bisacsh
082 0 4 $a 515.83 $2 23
090 $a QA314 $b .M251 2015
100 1 $a Malinowska, Agnieszka B. $3 677070
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 208302
650 0 $a Calculus of variations. $3 191127
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 274198
650 2 4 $a Control. $3 349080
650 2 4 $a Mathematical Methods in Physics. $3 273796
650 2 4 $a Game Theory/Mathematical Methods. $3 274396
650 2 4 $a Mathematical Modeling and Industrial Mathematics. $3 274070
650 2 4 $a Systems Theory, Control. $3 274654
700 1 $a Odzijewicz, Tatiana. $3 714414
700 1 $a Torres, Delfim F.M. $3 677071
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in applied sciences and technology. $3 557662
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-14756-7
950 $a Mathematics and Statistics (Springer-11649)