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We study fractional variational problems in terms of a generalized fractionalintegral with Lagrangians depending on classical derivatives, generalizedfractional integrals and derivatives. We obtain necessary optimality conditionsfor the basic and isoperimetric problems, as well as natural boundaryconditions for free boundary value problems. The fractional action-likevariational approach (FALVA) is extended and some applications to Physicsdiscussed.

Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics