| Nome: | Descrição: | Tamanho: | Formato: | |
|---|---|---|---|---|
| 324.73 KB | Adobe PDF |
Orientador(es)
Resumo(s)
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.
Descrição
Palavras-chave
Calculus of variations Euler-Lagrange equation Fractional difference calculus Fractional summation by parts Legendre necessary condition Natural boundary conditions Time scale hZ
Contexto Educativo
Citação
Editora
Elsevier