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math.OC2014
Existence of minimizers for generalized Lagrangian functionals and a necessary optimality condition --- Application to fractional variational problems
Loïc Bourdin, Tatiana Odzijewicz, Delfim F. M. Torres
We study dynamic minimization problems of the calculus of variations with generalized Lagrangian functionals that depend on a general linear operator and defined on bounded-tim…
math.OC2014★ 1 cited
Fractional fundamental lemma and fractional integration by parts formula -- Applications to critical points of Bolza functionals and to linear boundary value problems
Loïc Bourdin, Dariusz Idczak
In the first part of the paper, we prove a fractional fundamental (du Bois-Reymond) lemma and a fractional variant of the integration by parts formula. The proof of the second resu…