Publicação
Discrete-time fractional variational problems
| 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. |
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| 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 |
| 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. |
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