The Existence and Uniqueness of a Class of Fractional Differential Equations
By using inequalities, fixed point theorems, and lower and upper solution method, the existence and uniqueness of a class of fractional initial value problems, D0+qx(t)=f(t,x(t), D0+q-1x(t)), t∈(0,T), x(0)=0, D0+q-1x(0)=x0, are discussed, where f∈C([0,T]×R2,R),D0+qx(t) is the standard Riemann-L...
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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/10.1155/2014/486040 |
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| author | Zhanbing Bai Sujing Sun YangQuan Chen |
| author_facet | Zhanbing Bai Sujing Sun YangQuan Chen |
| author_sort | Zhanbing Bai |
| collection | DOAJ |
| description | By using inequalities, fixed point theorems, and lower and upper solution method, the existence and uniqueness of a class of fractional initial value problems, D0+qx(t)=f(t,x(t), D0+q-1x(t)), t∈(0,T), x(0)=0, D0+q-1x(0)=x0, are discussed, where f∈C([0,T]×R2,R),D0+qx(t) is the standard Riemann-Liouville fractional derivative, 1<q<2. Some mistakes in the literature are pointed out and some new inequalities and existence and uniqueness results are obtained. |
| format | Article |
| id | doaj-art-aba89ae837864f85b05f6bd377461f93 |
| 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-aba89ae837864f85b05f6bd377461f932025-02-03T01:31:37ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/486040486040The Existence and Uniqueness of a Class of Fractional Differential EquationsZhanbing Bai0Sujing Sun1YangQuan Chen2College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, ChinaSchool of Engineering, University of California, Merced, CA 95343, USABy using inequalities, fixed point theorems, and lower and upper solution method, the existence and uniqueness of a class of fractional initial value problems, D0+qx(t)=f(t,x(t), D0+q-1x(t)), t∈(0,T), x(0)=0, D0+q-1x(0)=x0, are discussed, where f∈C([0,T]×R2,R),D0+qx(t) is the standard Riemann-Liouville fractional derivative, 1<q<2. Some mistakes in the literature are pointed out and some new inequalities and existence and uniqueness results are obtained.http://dx.doi.org/10.1155/2014/486040 |
| spellingShingle | Zhanbing Bai Sujing Sun YangQuan Chen The Existence and Uniqueness of a Class of Fractional Differential Equations Abstract and Applied Analysis |
| title | The Existence and Uniqueness of a Class of Fractional Differential Equations |
| title_full | The Existence and Uniqueness of a Class of Fractional Differential Equations |
| title_fullStr | The Existence and Uniqueness of a Class of Fractional Differential Equations |
| title_full_unstemmed | The Existence and Uniqueness of a Class of Fractional Differential Equations |
| title_short | The Existence and Uniqueness of a Class of Fractional Differential Equations |
| title_sort | existence and uniqueness of a class of fractional differential equations |
| url | http://dx.doi.org/10.1155/2014/486040 |
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