Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations
We discuss the initial value problem for the nonlinear fractional differential equation L(D)u=f(t,u), t∈(0,1], u(0)=0, where L(D)=Dsn-an-1Dsn-1-⋯-a1Ds1, 0<s1<s2<⋯<sn<1, and aj<0, j=1,2,…,n-1, Dsj is the standard Riemann-Liouville fractional derivative and f:[0,1]×ℝ→ℝ is a given c...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/615230 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849684789453389824 |
|---|---|
| author | Qiuping Li Shurong Sun Ping Zhao Zhenlai Han |
| author_facet | Qiuping Li Shurong Sun Ping Zhao Zhenlai Han |
| author_sort | Qiuping Li |
| collection | DOAJ |
| description | We discuss the initial value problem for the nonlinear fractional differential equation L(D)u=f(t,u), t∈(0,1], u(0)=0, where L(D)=Dsn-an-1Dsn-1-⋯-a1Ds1, 0<s1<s2<⋯<sn<1, and aj<0, j=1,2,…,n-1, Dsj is the standard Riemann-Liouville fractional derivative and f:[0,1]×ℝ→ℝ is a given continuous function. We extend the basic theory of differential equation, the method of upper and lower solutions, and monotone iterative technique to the initial value problem. Some existence and uniqueness results are established. |
| format | Article |
| id | doaj-art-c646bbb1b46544d28fbd7fa244f3ce23 |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c646bbb1b46544d28fbd7fa244f3ce232025-08-20T03:23:22ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/615230615230Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential EquationsQiuping Li0Shurong Sun1Ping Zhao2Zhenlai Han3School of Mathematical Sciences, University of Jinan, Shandong, Jinan 250022, ChinaSchool of Mathematical Sciences, University of Jinan, Shandong, Jinan 250022, ChinaSchool of Control Science and Engineering, University of Jinan, Shandong, Jinan 250022, ChinaSchool of Mathematical Sciences, University of Jinan, Shandong, Jinan 250022, ChinaWe discuss the initial value problem for the nonlinear fractional differential equation L(D)u=f(t,u), t∈(0,1], u(0)=0, where L(D)=Dsn-an-1Dsn-1-⋯-a1Ds1, 0<s1<s2<⋯<sn<1, and aj<0, j=1,2,…,n-1, Dsj is the standard Riemann-Liouville fractional derivative and f:[0,1]×ℝ→ℝ is a given continuous function. We extend the basic theory of differential equation, the method of upper and lower solutions, and monotone iterative technique to the initial value problem. Some existence and uniqueness results are established.http://dx.doi.org/10.1155/2012/615230 |
| spellingShingle | Qiuping Li Shurong Sun Ping Zhao Zhenlai Han Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations Abstract and Applied Analysis |
| title | Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations |
| title_full | Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations |
| title_fullStr | Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations |
| title_full_unstemmed | Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations |
| title_short | Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations |
| title_sort | existence and uniqueness of solutions for initial value problem of nonlinear fractional differential equations |
| url | http://dx.doi.org/10.1155/2012/615230 |
| work_keys_str_mv | AT qiupingli existenceanduniquenessofsolutionsforinitialvalueproblemofnonlinearfractionaldifferentialequations AT shurongsun existenceanduniquenessofsolutionsforinitialvalueproblemofnonlinearfractionaldifferentialequations AT pingzhao existenceanduniquenessofsolutionsforinitialvalueproblemofnonlinearfractionaldifferentialequations AT zhenlaihan existenceanduniquenessofsolutionsforinitialvalueproblemofnonlinearfractionaldifferentialequations |