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Fractional calculus of variations in terms of a generalized fractional integral...
Odzijewicz, T.; Malinowska, A.B.; Torres, D.F.M.We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, as well as natural boundary conditions for free-boundary value problems. The fractional action-like variational approach (FALVA) is extended...
Fractional calculus of variations for double integrals
Odzijewicz, T.; Torres, D.F.M.We consider fractional isoperimetric problems of calculus of variations with double integrals via the recent modified Riemann-Liouville approach. A necessary optimality condition of Euler-Lagrange type, in the form of a multitime fractional PDE, is proved, as well as a sufficient condition and fractional natural boundary conditions. © Balkan Society of Geometers, Geometry Balkan Press 2011.
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