Existence of a weak solution for fractional Euler-Lagrange equations

In this paper, we state with a variational method a general theorem providing the existence of a weak solution $u$ for fractional Euler-Lagrange equations of the type: $\dfrac{\partial L}{\partial x} (u,D^α_- u,t) + D^α_+ (\dfrac{\partial L}{\partial y} (u,D^α_- u,t)) = 0$ on a real interval $[a,b]$ and where $D^α_-$ and $D^α_+$ are the fractional derivatives of Riemann-Liouville of order $0 < α< 1$.

No reviews yet.

No comments yet.