On discrete sequential fractional boundary value problems
In this paper, we analyze several different types of discrete sequential fractional boundary value problems. Our prototype equation is − Δ μ 1 Δ μ 2 Δ μ 3 y ( t ) = f ( t + μ 1 + μ 2 + μ 3 − 1 , y ( t + μ 1 + μ 2 + μ 3 − 1 ) ) subject to the conjugate boundary conditions y ( 0 ) = 0 = y ( b + 2 ) ,...
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| Published in | Journal of mathematical analysis and applications Vol. 385; no. 1; pp. 111 - 124 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
2012
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| Subjects | |
| Online Access | Get full text |
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| Abstract | In this paper, we analyze several different types of discrete sequential fractional boundary value problems. Our prototype equation is
−
Δ
μ
1
Δ
μ
2
Δ
μ
3
y
(
t
)
=
f
(
t
+
μ
1
+
μ
2
+
μ
3
−
1
,
y
(
t
+
μ
1
+
μ
2
+
μ
3
−
1
)
)
subject to the conjugate boundary conditions
y
(
0
)
=
0
=
y
(
b
+
2
)
, where
f
:
[
1
,
b
+
1
]
N
0
×
R
→
[
0
,
+
∞
)
is a continuous function and
μ
1
,
μ
2
,
μ
3
∈
(
0
,
1
)
satisfy
1
<
μ
2
+
μ
3
<
2
and
1
<
μ
1
+
μ
2
+
μ
3
<
2
. We also obtain results for delta–nabla discrete fractional boundary value problems. As an application of our analysis, we give conditions under which such problems will admit at least one positive solution. |
|---|---|
| AbstractList | In this paper, we analyze several different types of discrete sequential fractional boundary value problems. Our prototype equation is
−
Δ
μ
1
Δ
μ
2
Δ
μ
3
y
(
t
)
=
f
(
t
+
μ
1
+
μ
2
+
μ
3
−
1
,
y
(
t
+
μ
1
+
μ
2
+
μ
3
−
1
)
)
subject to the conjugate boundary conditions
y
(
0
)
=
0
=
y
(
b
+
2
)
, where
f
:
[
1
,
b
+
1
]
N
0
×
R
→
[
0
,
+
∞
)
is a continuous function and
μ
1
,
μ
2
,
μ
3
∈
(
0
,
1
)
satisfy
1
<
μ
2
+
μ
3
<
2
and
1
<
μ
1
+
μ
2
+
μ
3
<
2
. We also obtain results for delta–nabla discrete fractional boundary value problems. As an application of our analysis, we give conditions under which such problems will admit at least one positive solution. |
| Author | Goodrich, Christopher S. |
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| Snippet | In this paper, we analyze several different types of discrete sequential fractional boundary value problems. Our prototype equation is
−
Δ
μ
1
Δ
μ
2
Δ
μ
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y
(... |
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| SubjectTerms | Boundary value problem Cone Discrete fractional calculus Positive solution Sequential fractional difference |
| Title | On discrete sequential fractional boundary value problems |
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