Existence and Uniqueness of Positive Solutions for a Fractional Switched System
We discuss the existence and uniqueness of positive solutions for the following fractional switched system: (Dc0+αu(t)+fσ(t)(t,u(t))+gσ(t)(t,u(t))=0, t∈J=[0,1]); (u(0)=u′′(0)=0,u(1)=∫01u(s) ds), where Dc0+α is the Caputo fractional derivative with 2<α≤3, σ(t):J→{1,2,…,N} is a piecewise constant...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/828721 |
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| author | Zhi-Wei Lv Bao-Feng Chen |
| author_facet | Zhi-Wei Lv Bao-Feng Chen |
| author_sort | Zhi-Wei Lv |
| collection | DOAJ |
| description | We discuss the existence and uniqueness of positive solutions for the following fractional switched system: (Dc0+αu(t)+fσ(t)(t,u(t))+gσ(t)(t,u(t))=0, t∈J=[0,1]); (u(0)=u′′(0)=0,u(1)=∫01u(s) ds), where Dc0+α is the Caputo fractional derivative with 2<α≤3, σ(t):J→{1,2,…,N} is a piecewise constant function depending on t, and ℝ+=[0,+∞), fi,gi∈C[J×ℝ+,ℝ+], i=1,2,…,N. Our results are based on a fixed point theorem of a sum operator and contraction mapping principle. Furthermore, two examples are also given to illustrate the results. |
| format | Article |
| id | doaj-art-9997eb64ece2482da70fd0b4b102bf61 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9997eb64ece2482da70fd0b4b102bf612025-02-03T05:46:45ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/828721828721Existence and Uniqueness of Positive Solutions for a Fractional Switched SystemZhi-Wei Lv0Bao-Feng Chen1Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450001, ChinaDepartment of Mathematics and Physics, Anyang Institute of Technology, Anyang, Henan 455000, ChinaWe discuss the existence and uniqueness of positive solutions for the following fractional switched system: (Dc0+αu(t)+fσ(t)(t,u(t))+gσ(t)(t,u(t))=0, t∈J=[0,1]); (u(0)=u′′(0)=0,u(1)=∫01u(s) ds), where Dc0+α is the Caputo fractional derivative with 2<α≤3, σ(t):J→{1,2,…,N} is a piecewise constant function depending on t, and ℝ+=[0,+∞), fi,gi∈C[J×ℝ+,ℝ+], i=1,2,…,N. Our results are based on a fixed point theorem of a sum operator and contraction mapping principle. Furthermore, two examples are also given to illustrate the results.http://dx.doi.org/10.1155/2014/828721 |
| spellingShingle | Zhi-Wei Lv Bao-Feng Chen Existence and Uniqueness of Positive Solutions for a Fractional Switched System Abstract and Applied Analysis |
| title | Existence and Uniqueness of Positive Solutions for a Fractional Switched System |
| title_full | Existence and Uniqueness of Positive Solutions for a Fractional Switched System |
| title_fullStr | Existence and Uniqueness of Positive Solutions for a Fractional Switched System |
| title_full_unstemmed | Existence and Uniqueness of Positive Solutions for a Fractional Switched System |
| title_short | Existence and Uniqueness of Positive Solutions for a Fractional Switched System |
| title_sort | existence and uniqueness of positive solutions for a fractional switched system |
| url | http://dx.doi.org/10.1155/2014/828721 |
| work_keys_str_mv | AT zhiweilv existenceanduniquenessofpositivesolutionsforafractionalswitchedsystem AT baofengchen existenceanduniquenessofpositivesolutionsforafractionalswitchedsystem |