Abstract
AbstractWe deal with the following Riemann–Liouville fractional nonlinear boundary value problem: $$ \textstyle\begin{cases} \mathcal{D}^{\alpha }v(x)+f(x,v(x))=0, & 2< \alpha \leq 3, x\in (0,1), \\ v(0)=v^{\prime }(0)=v(1)=0. \end{cases} $$
{
D
α
v
(
x
)
+
f
(
x
,
v
(
x
)
)
=
0
,
2
<
α
≤
3
,
x
∈
(
0
,
1
)
,
v
(
0
)
=
v
′
(
0
)
=
v
(
1
)
=
0
.
Under mild assumptions, we prove the existence of a unique continuous solution v to this problem satisfying $$ \bigl\vert v(x) \bigr\vert \leq cx^{\alpha -1}(1-x)\quad\text{for all }x \in [ 0,1]\text{ and some }c>0. $$
|
v
(
x
)
|
≤
c
x
α
−
1
(
1
−
x
)
for all
x
∈
[
0
,
1
]
and some
c
>
0
.
Our results improve those obtained by Zou and He (Appl. Math. Lett. 74:68–73, 2017).
Funder
Deanship of Scientific Research, King Saud University
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Cited by
4 articles.
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