Abstract
In this paper, we consider the non-separated boundary value problem for system of nonlinear Riemann–Liouville fractional differential equations
D
0
+
α
x
(
t
)
+
λ
f
(
t
,
x
(
t
)
,
y
(
t
)
)
=
0
,
0
<
t
<
1
,
D
0
+
α
y
(
t
)
+
μ
g
(
t
,
x
(
t
)
,
y
(
t
)
)
=
0
,
0
<
t
<
1
,
subject to the boundary conditions
x
(
0
)
=
y
(
0
)
=
0
,
u
1
D
0
+
β
x
(
1
)
=
v
1
D
0
+
β
y
(
ξ
)
,
u
2
D
0
+
β
y
(
1
)
=
v
2
D
0
+
β
x
(
η
)
,
η
,
ξ
∈
(
0
,
1
)
,
where the coefficients
u
i
,
v
i
,
i
=
1
,
2
are real positive constants, we give sufficient conditions on
λ
,
μ
,
f
and
g
such that the system has no positive solutions. An example is given to demonstrate the main result.