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Title: Discrete direct methods in the fractional calculus of variations
Author: Pooseh, S.
Almeida, R.
Torres, D.F.M.
Keywords: Direct methods
Fractional calculus
Fractional calculus of variations
Mesh points
Minimization problems
Riemann-Liouville fractional derivatives
Static optimization
Variational problems
Mathematical models
Issue Date: Sep-2013
Publisher: Elsevier
Abstract: 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 Grünwald-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.
Peer review: yes
DOI: 10.1016/j.camwa.2013.01.045
ISSN: 0898-1221
Appears in Collections:CIDMA - Artigos
DMat - Artigos

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