TY: JOUR
T1 - Necessary optimality conditions for fractional difference problems of the calculus of variations
A1 - Bastos, N.R.O.
A1 - Ferreira, R.A.C.
A1 - Torres, D.F.M.
N2 - 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.
UR - https://ria.ua.pt/handle/10773/4074
Y1 - 2011
PB - American Institute of Mathematical Sciences (AIMS)