Advanced methods in the fractional calculus of variations: [electronic resource] /: Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres.

Malinowska, Agnieszka B.,; Odzijewicz, Tatiana,; Torres, Delfim F. M.,

doi:10.1007/978-3-319-14756-7

Advanced methods in the fractional calculus of variations [electronic resource] / Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres.

Malinowska, Agnieszka B., author.; Odzijewicz, Tatiana, author.; Torres, Delfim F. M., author.

2015

QA314

Available Online

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Title

Advanced methods in the fractional calculus of variations [electronic resource] / Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres.

Author

Malinowska, Agnieszka B., author.

ISBN

9783319147567 electronic book
3319147560 electronic book
9783319147550

DOI

https://doi.org/10.1007/978-3-319-14756-7

Published

Cham : Springer, [2015]

Language

English

Description

1 online resource (xii, 135 pages).

Item Number

10.1007/978-3-319-14756-7 doi

Call Number

QA314

Dewey Decimal Classification

515/.83

Summary

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 Eulerℓ́ℓLagrange 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 Eulerℓ́ℓLagrange 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 Sturmℓ́ℓLiouville 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.

Bibliography, etc. Note

Includes bibliographical references and index.

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Access limited to authorized users.

Source of Description

Online resource; title from PDF title page (SpringerLink, viewed February 11, 2015).

Added Author

Odzijewicz, Tatiana, author.
Torres, Delfim F. M., author.

Series

SpringerBriefs in applied sciences and technology.

Available in Other Form

Print version: 9783319147550