Existence of a weak solution for fractional Euler-Lagrange equations
Abstract
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:
∂L
∂x
(u,
D
α
−
u,t)+
D
α
+
(
∂L
∂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
.