Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators
We consider the following state dependent boundary-value problem D0+αy(t)-pD0+βg(t,y(σ(t)))+f(t,y(τ(t)))=0, 0<t<1; y(0)=0, ηy(σ(1))=y(1), where Dα is the standard Riemann-Liouville fractional derivative of order 1<α<2, 0<η<1, p≤0, 0<β<1, β+1-α≥0 the function g is defined as g...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/263748 |
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| author | Dongyuan Liu Zigen Ouyang Huilan Wang |
| author_facet | Dongyuan Liu Zigen Ouyang Huilan Wang |
| author_sort | Dongyuan Liu |
| collection | DOAJ |
| description | We consider the following state dependent boundary-value problem D0+αy(t)-pD0+βg(t,y(σ(t)))+f(t,y(τ(t)))=0, 0<t<1; y(0)=0, ηy(σ(1))=y(1), where Dα is the standard Riemann-Liouville fractional derivative of order 1<α<2, 0<η<1, p≤0, 0<β<1, β+1-α≥0 the function g is defined as g(t,u):[0,1]×[0,∞)→[0,∞), and g(0,0)=0 the function f is defined as f(t,u):[0,1]×[0,∞)→[0,∞)σ(t), τ(t) are continuous on t and 0≤σ(t), τ(t)≤t. Using Banach contraction mapping principle and Leray-Schauder continuation principle, we obtain some sufficient conditions for the existence and uniqueness of the positive solutions for the above fractional order differential equations, which extend some references. |
| format | Article |
| id | doaj-art-0c2b8efcaa144ecf86ecc33b0bf7fc8d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0c2b8efcaa144ecf86ecc33b0bf7fc8d2025-02-03T06:44:51ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/263748263748Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential OperatorsDongyuan Liu0Zigen Ouyang1Huilan Wang2School of Mathematics and Physics, University of South China, Hengyang 421001, ChinaSchool of Mathematics and Physics, University of South China, Hengyang 421001, ChinaSchool of Mathematics and Physics, University of South China, Hengyang 421001, ChinaWe consider the following state dependent boundary-value problem D0+αy(t)-pD0+βg(t,y(σ(t)))+f(t,y(τ(t)))=0, 0<t<1; y(0)=0, ηy(σ(1))=y(1), where Dα is the standard Riemann-Liouville fractional derivative of order 1<α<2, 0<η<1, p≤0, 0<β<1, β+1-α≥0 the function g is defined as g(t,u):[0,1]×[0,∞)→[0,∞), and g(0,0)=0 the function f is defined as f(t,u):[0,1]×[0,∞)→[0,∞)σ(t), τ(t) are continuous on t and 0≤σ(t), τ(t)≤t. Using Banach contraction mapping principle and Leray-Schauder continuation principle, we obtain some sufficient conditions for the existence and uniqueness of the positive solutions for the above fractional order differential equations, which extend some references.http://dx.doi.org/10.1155/2015/263748 |
| spellingShingle | Dongyuan Liu Zigen Ouyang Huilan Wang Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators Abstract and Applied Analysis |
| title | Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators |
| title_full | Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators |
| title_fullStr | Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators |
| title_full_unstemmed | Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators |
| title_short | Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators |
| title_sort | positive solutions for class of state dependent boundary value problems with fractional order differential operators |
| url | http://dx.doi.org/10.1155/2015/263748 |
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