2014-10-23T21:34:57Zhttp://www.hindawi.com/oai-pmh/oai.aspxoai:hindawi.com:10.1155/2011/391971
2011-06-13T11:37:16Z
HINDAWI.AAA:2011Existence of Positive Solutions for a Class of Delay Fractional Differential Equations with Generalization to N-Term
Azizollah Babakhani
Dumitru Baleanu
We established the existence of a positive solution of nonlinear
fractional differential equations
𝔏
(
𝐷
)
[
𝑥
(
𝑡
)
−
𝑥
(
0
)
]
=
𝑓
(
𝑡
,
𝑥
𝑡
)
,
𝑡
∈
(
0
,
𝑏
]
with finite delay
𝑥
(
𝑡
)
=
𝜔
(
𝑡
)
,
𝑡
∈
[
−
𝜏
,
0
]
, where
l
i
m
𝑡
→
0
𝑓
(
𝑡
,
𝑥
𝑡
)
=
+
∞
, that is,
𝑓
is singular at
𝑡
=
0
and
𝑥
𝑡
∈
𝐶
(
[
−
𝜏
,
0
]
,
ℝ
≥
0
)
. The operator of
𝔏
(
𝐷
)
involves the
Riemann-Liouville fractional derivatives. In this problem, the initial conditions with
fractional order and some relations among them were considered. The analysis rely
on the alternative of the Leray-Schauder fixed point theorem, the Banach fixed point
theorem, and the Arzela-Ascoli theorem in a cone.
Abstract and Applied Analysis
2011
Research Article
http://dx.doi.org/10.1155/2011/391971
en
Copyright © 2011 Azizollah Babakhani and Dumitru Baleanu.