Discrete-time fractional variational problems

• Type: Article in International Scientific Journal
• Date: 2011

Authors

Bastos, NRO (Author) Other; Ferreira, RAC (Author) Other; Torres, DFM (Author) Other

Journal

Title: Signal Processing

Vol. 91

Pages: 513-524

ISSN: 0165-1684

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 129 Citations

Scopus - 171 Citations

Other information

Authenticus ID: P-002-TQT

DOI: 10.1016/j.sigpro.2010.05.001

Abstract (EN): We introduce a discrete-time fractional calculus of variations on the time scale (hZ)(a), a is an element of R,h > 0. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They show that solutions to the considered fractional problems become the classical discrete-time solutions when the fractional order of the discrete-derivatives are integer values, and that they converge to the fractional continuous-time solutions when h tends to zero. Our Legendre type condition is useful to eliminate false candidates identified via the Euler-Lagrange fractional equation.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 12