Existence of a weak solution for fractional Euler–Lagrange equations
Résumé
We derive sufficient conditions ensuring the existence of a weak solution u for fractional Euler-Lagrange equations of the type:
∂L/∂x (u,Dα−[u],t) + Dα+[ ∂L/∂y (u,Dα−[u],t) ] = 0,
on a real interval [a, b] and where Dα− and Dα+ are the fractional derivatives of Riemann-Liouville of order 0<α<1.
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