Existence and uniqueness of positive solutions for boundary value problems of a fractional differential equation with a parameter

Chen YANG

Article Details

Existence and uniqueness of positive solutions for boundary value problems of a fractional differential equation with a parameter

Authors:

Chen YANG

Publisher:

Hacettepe University

Main Topics:

Mathematics

Journal:

Hacettepe Journal of Mathematics and Statistics 2015 Vol.44 Issue 3, pp.659-667

Document Type:

Article

Publication Date:

5/2015

Document Language:

English

Document ID (Org No.):

2000453050

Frequency:

Bimonthly

eISSN:

2651-477X

pISSN:

2651-477X

Abstract:

 

In this paper, we are concerned with the existence and uniqueness
of positive solutions for the following nonlinear fractional two-point
boundary value problem

D
α
0+u(t) + λf(t, u(t), u(t)) = 0, 0 < t < 1, 2 < α ≤ 3,
u(0) = u
0
(0) = u
0
(1) = 0,
where D
α
0+ is the standard Riemann-Liouville fractional derivative, and
λ is a positive parameter. Our analysis relies on a fixed point theorem
and some properties of eigenvalue problems for a class of general mixed
monotone operators. Our results can not only guarantee the existence
of a unique positive solution, but also be applied to construct an iterative scheme for approximating it. An example is given to illustrate the
main results.

Article Details

Existence and uniqueness of positive solutions for boundary value problems of a fractional differential equation with a parameter

Authors: Chen YANG

Publisher: Hacettepe University

Main Topics: Mathematics

Journal: Hacettepe Journal of Mathematics and Statistics 2015 Vol.44 Issue 3, pp.659-667

Document Type: Article

Publication Date: 5/2015

Document Language: English

Document ID (Org No.): 2000453050

Frequency: Bimonthly

eISSN: 2651-477X

pISSN: 2651-477X

Issues

Authors:

Chen YANG

Publisher:

Hacettepe University

Main Topics:

Mathematics

Journal:

Hacettepe Journal of Mathematics and Statistics 2015 Vol.44 Issue 3, pp.659-667

Document Type:

Article

Publication Date:

5/2015

Document Language:

English

Document ID (Org No.):

2000453050

Frequency:

Bimonthly

eISSN:

2651-477X

pISSN:

2651-477X