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Title: Necessary optimality conditions for fractional difference problems of the calculus of variations
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
Issue Date: 2011
Publisher: American Institute of Mathematical Sciences (AIMS)
Abstract: We introduce a discrete-time fractional calculus of variations. 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 the solutions of the fractional problems coincide with the solutions of the corresponding non-fractional variational problems when the order of the discrete derivatives is an integer value.
Peer review: yes
ISSN: 1078-0947
Appears in Collections:DMat - Artigos

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