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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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| 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. |
| format | Article |
| id | doaj-art-dfb2c95655d94828a0437d9908ef094c |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| 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 |
| work_keys_str_mv | AT wenjiema theeigenvalueproblemforcaputotypefractionaldifferentialequationwithriemannstieltjesintegralboundaryconditions AT yujuncui theeigenvalueproblemforcaputotypefractionaldifferentialequationwithriemannstieltjesintegralboundaryconditions AT wenjiema eigenvalueproblemforcaputotypefractionaldifferentialequationwithriemannstieltjesintegralboundaryconditions AT yujuncui eigenvalueproblemforcaputotypefractionaldifferentialequationwithriemannstieltjesintegralboundaryconditions |