Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations
In this paper, we are concerned with the nonlinear differential equation of fractional order D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , 1 < α ≤ 2 , where D 0 + α is the standard Riemann–Liouville fractional order derivative, subject to the boundary conditions u ( 0 ) = 0 , D 0 +...
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| Published in | Computers & mathematics with applications (1987) Vol. 59; no. 3; pp. 1363 - 1375 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.02.2010
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0898-1221 1873-7668 |
| DOI | 10.1016/j.camwa.2009.06.029 |
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| Abstract | In this paper, we are concerned with the nonlinear differential equation of fractional order
D
0
+
α
u
(
t
)
+
f
(
t
,
u
(
t
)
)
=
0
,
0
<
t
<
1
,
1
<
α
≤
2
,
where
D
0
+
α
is the standard Riemann–Liouville fractional order derivative, subject to the boundary conditions
u
(
0
)
=
0
,
D
0
+
β
u
(
1
)
=
a
D
0
+
β
u
(
ξ
)
.
We obtain the existence and multiplicity results of positive solutions by using some fixed point theorems. |
|---|---|
| AbstractList | In this paper, we are concerned with the nonlinear differential equation of fractional order
D
0
+
α
u
(
t
)
+
f
(
t
,
u
(
t
)
)
=
0
,
0
<
t
<
1
,
1
<
α
≤
2
,
where
D
0
+
α
is the standard Riemann–Liouville fractional order derivative, subject to the boundary conditions
u
(
0
)
=
0
,
D
0
+
β
u
(
1
)
=
a
D
0
+
β
u
(
ξ
)
.
We obtain the existence and multiplicity results of positive solutions by using some fixed point theorems. |
| Author | Li, C.F. Zhou, Yong Luo, X.N. |
| Author_xml | – sequence: 1 givenname: C.F. surname: Li fullname: Li, C.F. email: cfli@xtu.edu.cn – sequence: 2 givenname: X.N. surname: Luo fullname: Luo, X.N. email: Luoxn@xtu.edu.cn – sequence: 3 givenname: Yong surname: Zhou fullname: Zhou, Yong email: yzhou@xtu.edu.cn |
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| Keywords | Fractional differential equation Riemann–Liouville derivative Boundary value problem Carathéodory conditions Positive solution |
| Language | English |
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| Snippet | In this paper, we are concerned with the nonlinear differential equation of fractional order
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| SubjectTerms | Boundary value problem Carathéodory conditions Fractional differential equation Positive solution Riemann–Liouville derivative |
| Title | Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations |
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