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Formulation of Euler-Lagrange equations for fractional variational problems. (English) Zbl 1070.49013

The author gives an analogue of the Euler equation for the variational problem for the functional \(J[y]= \int_a^b F(x,y,y^{(\alpha)}_+, y^{(\beta)}_-)\; dx\) where \(y^{(\alpha)}_+\) and \( y^{(\beta)}_-\) stand, respectively, for the left-hand sided and right-hand sided fractional derivatives.

MSC:

49K05 Optimality conditions for free problems in one independent variable
26A33 Fractional derivatives and integrals
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