The Existence of Positive Solutions for Boundary Value Problem of the Fractional Sturm-Liouville Functional Differential Equation
Joint Authors
Han, Zhen-Lai
Sun, Shurong
Lu, Hongling
Li, Yanan
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-09-22
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
We study boundary value problems for the following nonlinear fractional Sturm-Liouville functional differential equations involving the Caputo fractional derivative: CDβ(p(t)CDαu(t)) + f(t,u(t-τ),u(t+θ))=0, t∈(0,1), CDαu(0)= CDαu(1)=( CDαu(0))=0, au(t)-bu′(t)=η(t), t∈[-τ,0], cu(t)+du′(t)=ξ(t), t∈[1,1+θ], where CDα, CDβ denote the Caputo fractional derivatives, f is a nonnegative continuous functional defined on C([-τ,1+θ],ℝ), 1<α≤2, 2<β≤3, 0<τ, θ<1/4 are suitably small, a,b,c,d>0, and η∈C([-τ,0],[0,∞)), ξ∈C([1,1+θ],[0,∞)).
By means of the Guo-Krasnoselskii fixed point theorem and the fixed point index theorem, some positive solutions are obtained, respectively.
As an application, an example is presented to illustrate our main results.
American Psychological Association (APA)
Li, Yanan& Sun, Shurong& Han, Zhen-Lai& Lu, Hongling. 2013. The Existence of Positive Solutions for Boundary Value Problem of the Fractional Sturm-Liouville Functional Differential Equation. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-20.
https://search.emarefa.net/detail/BIM-461610
Modern Language Association (MLA)
Li, Yanan…[et al.]. The Existence of Positive Solutions for Boundary Value Problem of the Fractional Sturm-Liouville Functional Differential Equation. Abstract and Applied Analysis No. 2013 (2013), pp.1-20.
https://search.emarefa.net/detail/BIM-461610
American Medical Association (AMA)
Li, Yanan& Sun, Shurong& Han, Zhen-Lai& Lu, Hongling. The Existence of Positive Solutions for Boundary Value Problem of the Fractional Sturm-Liouville Functional Differential Equation. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-20.
https://search.emarefa.net/detail/BIM-461610
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-461610