Applying periodic and anti-periodic boundary conditions in existence results of fractional differential equations via nonlinear contractive mappings
We introduce a notion of nonlinear cyclic orbital ( ξ − F ) -contraction and prove related results. With these results, we address the existence and uniqueness results with periodic/anti-periodic boundary conditions for: 1. The nonlinear multi-order fractional differential equation L ( D ) θ ( ς ) =...
Gespeichert in:
Veröffentlicht in: | Boundary value problems 2023-09, Vol.2023 (1), p.91-35, Article 91 |
---|---|
Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | We introduce a notion of nonlinear cyclic orbital
(
ξ
−
F
)
-contraction and prove related results. With these results, we address the existence and uniqueness results with periodic/anti-periodic boundary conditions for:
1. The nonlinear multi-order fractional differential equation
L
(
D
)
θ
(
ς
)
=
σ
(
ς
,
θ
(
ς
)
)
,
ς
∈
J
=
[
0
,
A
]
,
A
>
0
,
where
L
(
D
)
=
γ
w
c
D
δ
w
+
γ
w
−
1
c
D
δ
w
−
1
+
⋯
+
γ
1
c
D
δ
1
+
γ
0
c
D
δ
0
,
γ
♭
∈
R
(
♭
=
0
,
1
,
2
,
3
,
…
,
w
)
,
γ
w
≠
0
,
0
≤
δ
0
<
δ
1
<
δ
2
<
⋯
<
δ
w
−
1
<
δ
w
<
1
;
2. The nonlinear multi-term fractional delay differential equation
L
(
D
)
θ
(
ς
)
=
σ
(
ς
,
θ
(
ς
)
,
θ
(
ς
−
τ
)
)
,
ς
∈
J
=
[
0
,
A
]
,
A
>
0
;
θ
(
ς
)
=
σ
¯
(
ς
)
,
ς
∈
[
−
τ
,
0
]
,
where
L
(
D
)
=
γ
w
c
D
δ
w
+
γ
w
−
1
c
D
δ
w
−
1
+
⋯
+
γ
1
c
D
δ
1
+
γ
0
c
D
δ
0
,
γ
♭
∈
R
(
♭
=
0
,
1
,
2
,
3
,
…
,
w
)
,
γ
w
≠
0
,
0
≤
δ
0
<
δ
1
<
δ
2
<
⋯
<
δ
w
−
1
<
δ
w
<
1
;
moreover, here
D
δ
c
is predominantly called Caputo fractional derivative of order
δ
. |
---|---|
ISSN: | 1687-2770 1687-2762 1687-2770 |
DOI: | 10.1186/s13661-023-01778-3 |