TY: CONF
T1 - Discrete Direct Methods in the Fractional Calculus of Variations
A1 - Pooseh, Shakoor
A1 - Almeida, Ricardo
A1 - Torres, Delfim F. M.
N2 - Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear
in the problem. This article generalizes the same idea for fractional variational problems.
We consider a minimization problem with a Lagrangian that depends on the left Riemann?
Liouville fractional derivative. Using the Gr¨unwald?Letnikov definition, we approximate the objective functional in an equispaced grid as a multi-variable function of the values of the unknown function on mesh points. The problem is then transformed to an ordinary static optimization problem. The solution to the latter problem gives an approximation to the original fractional problem on mesh points.
UR - https://ria.ua.pt/handle/10773/10514
Y1 - 2012
PB - FDA