Abstract
In this paper, we investigate the existence and uniqueness of solutions for a differential equation of fractional-order
q
∈
(
1
,
2
]
subject to nonlocal boundary conditions involving Caputo derivative of the form
x
(
0
)
=
δ
x
(
σ
)
,
a
c
D
μ
x
(
ϱ
1
)
+
b
c
D
μ
x
(
ϱ
2
)
=
c
∫
β
1
β
2
c
D
μ
x
(
s
)
d
s
,
0
<
ϱ
1
<
σ
<
β
1
<
β
2
<
ϱ
2
<
1
,
0
<
μ
<
1
, and
δ
,
a
,
b
,
c
are real constants. We make use of some standard tools of fixed point theory to obtain the desired results which are well illustrated with the aid of examples.