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Necessary optimality conditions for fractional action-like integrals of variational calculus with Riemann-Liouville derivatives of order (\(\alpha, \beta\)). (English) Zbl 1177.49036

Summary: We derive Euler-Lagrange-type equations for fractional action-like integrals of the calculus of variations which depend on the Riemann-Liouville derivatives of order \((\alpha, \beta)\), \(\alpha>0\), \(\beta > 0\) recently introduced by Cresson. Some interesting consequences are obtained and discussed.

MSC:

49K15 Optimality conditions for problems involving ordinary differential equations
26A33 Fractional derivatives and integrals
49S05 Variational principles of physics
70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics
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