Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential Equation
By means of the method of quasi-lower and quasi-upper solutions and monotone iterative technique, we consider the nonlinear boundary value problems with Caputo fractional derivative and introduce two well-defined monotone sequences of quasi-lower and quasi-upper solutions which converge uniformly to...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/493164 |
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| _version_ | 1832568107449712640 |
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| author | Chaozhu Hu Bin Liu Songfa Xie |
| author_facet | Chaozhu Hu Bin Liu Songfa Xie |
| author_sort | Chaozhu Hu |
| collection | DOAJ |
| description | By means of the method of quasi-lower and quasi-upper solutions and monotone iterative technique,
we consider the nonlinear boundary value problems with Caputo fractional derivative and introduce
two well-defined monotone sequences of quasi-lower and quasi-upper solutions which converge
uniformly to the actual solution of the problem, and then the existence results of the solution for the
problems are established. A numerical iterative scheme is introduced to obtain an accurate approximate solution and to give one example to demonstrate the accuracy and efficiency of the new approach. |
| format | Article |
| id | doaj-art-d118a6a445dd45ca94fd2ae7fa08bb86 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d118a6a445dd45ca94fd2ae7fa08bb862025-02-03T00:59:50ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/493164493164Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential EquationChaozhu Hu0Bin Liu1Songfa Xie2School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, ChinaSchool of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, ChinaSchool of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, ChinaBy means of the method of quasi-lower and quasi-upper solutions and monotone iterative technique, we consider the nonlinear boundary value problems with Caputo fractional derivative and introduce two well-defined monotone sequences of quasi-lower and quasi-upper solutions which converge uniformly to the actual solution of the problem, and then the existence results of the solution for the problems are established. A numerical iterative scheme is introduced to obtain an accurate approximate solution and to give one example to demonstrate the accuracy and efficiency of the new approach.http://dx.doi.org/10.1155/2013/493164 |
| spellingShingle | Chaozhu Hu Bin Liu Songfa Xie Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential Equation Abstract and Applied Analysis |
| title | Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential Equation |
| title_full | Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential Equation |
| title_fullStr | Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential Equation |
| title_full_unstemmed | Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential Equation |
| title_short | Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential Equation |
| title_sort | monotone iterative solutions for nonlinear boundary value problems of fractional differential equation |
| url | http://dx.doi.org/10.1155/2013/493164 |
| work_keys_str_mv | AT chaozhuhu monotoneiterativesolutionsfornonlinearboundaryvalueproblemsoffractionaldifferentialequation AT binliu monotoneiterativesolutionsfornonlinearboundaryvalueproblemsoffractionaldifferentialequation AT songfaxie monotoneiterativesolutionsfornonlinearboundaryvalueproblemsoffractionaldifferentialequation |