Image of Advanced Methods in the Fractional Calculus of Variations
Bookmark Share

Text

Advanced Methods in the Fractional Calculus of Variations

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.

Availability

No copy data

Detail Information
Series Title
SpringerBriefs in Applied Sciences and Technology
Call Number
515.4 MAL a
Publisher
Cham, Switzerland : Springer.,
Collation
XII, 135
Language
English
ISBN/ISSN
978-3-319-14756-7
Classification
515.4
Content Type
text
Media Type
computer
Carrier Type
online resource
Edition
Ed. 1
Subject(s)
Calculus of Variations and Optimization
Control and Systems Theory
Specific Detail Info
-
Statement of Responsibility
Other Information
Cataloger
umi
Source
https://link.springer.com/content/pdf/10.1007/978-3-319-14756-7.pdf?pdf=button
Validator
-
Other version/related

No other version available

File Attachment
Comments
You must be logged in to post a comment