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Discrete-time fractional variational problems

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Resumo: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.
Autores principais:Bastos, N.R.O.
Outros Autores:Ferreira, R.A.C.; Torres, D.F.M.
Assunto:Calculus of variations Euler-Lagrange equation Fractional difference calculus Fractional summation by parts Legendre necessary condition Natural boundary conditions Time scale hZ
Ano:2011
País:Portugal
Tipo de documento:artigo
Tipo de acesso:acesso restrito
Instituição associada:Universidade de Aveiro
Idioma:inglês
Origem:RIA - Repositório Institucional da Universidade de Aveiro

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