The Eigenvalue Problem for Caputo Type Fractional Differential Equation with Riemann-Stieltjes Integral Boundary Conditions

In this paper, we investigate the eigenvalue problem for Caputo fractional differential equation with Riemann-Stieltjes integral boundary conditions Dc0+θp(y)+μf(t,p(y))=0, y∈[0,1], p(0)=p′′(0)=0, p(1)=∫01p(y)dA(y), where Dc0+θ is Caputo fractional derivative, θ∈(2,3], and f:[0,1]×[0,+∞)→[0,+∞) is c...

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Main Authors: Wenjie Ma, Yujun Cui
Format: Article
Language:English
Published: Wiley 2018-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2018/2176809
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author Wenjie Ma
Yujun Cui
author_facet Wenjie Ma
Yujun Cui
author_sort Wenjie Ma
collection DOAJ
description In this paper, we investigate the eigenvalue problem for Caputo fractional differential equation with Riemann-Stieltjes integral boundary conditions Dc0+θp(y)+μf(t,p(y))=0, y∈[0,1], p(0)=p′′(0)=0, p(1)=∫01p(y)dA(y), where Dc0+θ is Caputo fractional derivative, θ∈(2,3], and f:[0,1]×[0,+∞)→[0,+∞) is continuous. By using the Guo-Krasnoselskii’s fixed point theorem on cone and the properties of the Green’s function, some new results on the existence and nonexistence of positive solutions for the fractional differential equation are obtained.
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institution Kabale University
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language English
publishDate 2018-01-01
publisher Wiley
record_format Article
series Journal of Function Spaces
spelling doaj-art-dfb2c95655d94828a0437d9908ef094c2025-02-03T01:11:12ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/21768092176809The Eigenvalue Problem for Caputo Type Fractional Differential Equation with Riemann-Stieltjes Integral Boundary ConditionsWenjie Ma0Yujun Cui1Department of Applied Mathematics, Shandong University of Science and Technology, Qingdao 266590, ChinaState Key Laboratory of Mining Disaster Prevention and Control Co-Founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, ChinaIn this paper, we investigate the eigenvalue problem for Caputo fractional differential equation with Riemann-Stieltjes integral boundary conditions Dc0+θp(y)+μf(t,p(y))=0, y∈[0,1], p(0)=p′′(0)=0, p(1)=∫01p(y)dA(y), where Dc0+θ is Caputo fractional derivative, θ∈(2,3], and f:[0,1]×[0,+∞)→[0,+∞) is continuous. By using the Guo-Krasnoselskii’s fixed point theorem on cone and the properties of the Green’s function, some new results on the existence and nonexistence of positive solutions for the fractional differential equation are obtained.http://dx.doi.org/10.1155/2018/2176809
spellingShingle Wenjie Ma
Yujun Cui
The Eigenvalue Problem for Caputo Type Fractional Differential Equation with Riemann-Stieltjes Integral Boundary Conditions
Journal of Function Spaces
title The Eigenvalue Problem for Caputo Type Fractional Differential Equation with Riemann-Stieltjes Integral Boundary Conditions
title_full The Eigenvalue Problem for Caputo Type Fractional Differential Equation with Riemann-Stieltjes Integral Boundary Conditions
title_fullStr The Eigenvalue Problem for Caputo Type Fractional Differential Equation with Riemann-Stieltjes Integral Boundary Conditions
title_full_unstemmed The Eigenvalue Problem for Caputo Type Fractional Differential Equation with Riemann-Stieltjes Integral Boundary Conditions
title_short The Eigenvalue Problem for Caputo Type Fractional Differential Equation with Riemann-Stieltjes Integral Boundary Conditions
title_sort eigenvalue problem for caputo type fractional differential equation with riemann stieltjes integral boundary conditions
url http://dx.doi.org/10.1155/2018/2176809
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AT wenjiema eigenvalueproblemforcaputotypefractionaldifferentialequationwithriemannstieltjesintegralboundaryconditions
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