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Title: Discrete-time fractional variational problems
Author: Bastos, N.R.O.
Ferreira, R.A.C.
Torres, D.F.M.
Keywords: Calculus of variations
Euler-Lagrange equation
Fractional difference calculus
Fractional summation by parts
Legendre necessary condition
Natural boundary conditions
Time scale hZ
Issue Date: 2011
Publisher: Elsevier
Abstract: We introduce a discrete-time fractional calculus of variations on the time scale (hℤ)a,a∈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. © 2010 Elsevier B.V. All rights reserved.
Peer review: yes
ISSN: 0165-1684
Appears in Collections:DMat - Artigos

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