Abstract
We establish the existence and uniqueness of a positive solution
u
for the following fractional boundary value problem
:D
α
u
(
x
)
=
−
a
(
x
)
u
σ
(
x
)
,
x
∈
(
0
,
1
)
with the conditions
lim
x
→
0
+
x
2
−
α
u
(
x
)
=
0
,
u
(
1
)
=
0
, where
1
<
α
≤
2
,
σ
∈
(
−
1
,
1
)
, and
a
is a nonnegative continuous function on
(
0
,
1
)
that may be singular at
x
=
0
or
x
=
1
. We also give the global behavior of such a solution.