Browsing by Author "Bastos, N. R. O."
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- Discrete-time fractional variational problemsPublication . Bastos, N. R. O.; Ferreira, R. A. C.; Torres, D. F. M.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.
- Necessary optimality conditions for fractional difference problems of the calculus of variationsPublication . Bastos, N. R. O.; Ferreira, R. A. C.; Torres, D. F. M.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.