Bastos, N. R. O.Ferreira, R. A. C.Torres, D. F. M.2014-12-092014-12-0920111078-0947http://hdl.handle.net/10400.19/2434We 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.engCalculus of variationsEuler-Lagrange equationFractional difference calculusFractional summation by partsLegendre necessary conditionjournal article