Abstract
In this paper, we investigate the existence and uniqueness of solutions for the following class of multi-order fractional differential equations
D
β
1
γ
1
,
δ
1
⋯
D
β
n
γ
n
,
δ
n
u
(
t
)
:
=
∏
i
=
1
n
D
β
i
γ
i
,
δ
i
u
(
t
)
:
=
D
β
i
,
n
γ
i
,
δ
i
u
(
t
)
=
f
(
t
,
u
(
t
)
)
,
t
∈
[
0
,
1
]
,
u
(
0
)
=
0
,
∑
i
=
1
n
δ
i
⩽
1
,
γ
i
>
0
,
β
i
>
0
,
1
⩽
i
⩽
n
,
where
D
β
i
,
n
γ
i
,
δ
i
denotes the generalized Erdélyi–Kober operator of fractional derivative of order
δ
i
. Moreover, some properties concerning the positive, maximal, minimal, and continuation of solutions are obtained.