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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.

49K05Free problems in one independent variable (optimality conditions)
26A33Fractional derivatives and integrals (real functions)
Full Text: DOI
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