Positive Solutions for the Initial Value Problems of Fractional Evolution Equation
This paper discusses the existence of positive solutions for the initial value problem of fractional evolution equation with noncompact semigroup , ; in a Banach space , where denotes the Caputo fractional derivative of order , is a closed linear operator, generates an equicontinuous semigroup,...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/781404 |
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| _version_ | 1832552855167303680 |
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| author | Yue Liang Yu Ma Xiaoyan Gao |
| author_facet | Yue Liang Yu Ma Xiaoyan Gao |
| author_sort | Yue Liang |
| collection | DOAJ |
| description | This paper discusses the existence of positive solutions for the initial value problem of fractional evolution equation with noncompact semigroup , ; in a Banach space , where denotes the Caputo fractional derivative of order , is a closed linear operator, generates an equicontinuous semigroup, and is continuous. In the case where satisfies a weaker measure of noncompactness condition and a weaker boundedness condition, the existence results of positive and saturated mild solutions are obtained. Particularly, an existence result without using measure of noncompactness condition is presented in ordered and weakly sequentially complete Banach spaces. These results are very convenient for application. As an example, we study the partial differential equation of parabolic type of fractional order. |
| format | Article |
| id | doaj-art-62fddb12620b4f0a952807de3ea7d751 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-62fddb12620b4f0a952807de3ea7d7512025-02-03T05:57:39ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/781404781404Positive Solutions for the Initial Value Problems of Fractional Evolution EquationYue Liang0Yu Ma1Xiaoyan Gao2Science College of Gansu Agricultural University, Lanzhou 730070, ChinaScience College of Gansu Agricultural University, Lanzhou 730070, ChinaScience College of Gansu Agricultural University, Lanzhou 730070, ChinaThis paper discusses the existence of positive solutions for the initial value problem of fractional evolution equation with noncompact semigroup , ; in a Banach space , where denotes the Caputo fractional derivative of order , is a closed linear operator, generates an equicontinuous semigroup, and is continuous. In the case where satisfies a weaker measure of noncompactness condition and a weaker boundedness condition, the existence results of positive and saturated mild solutions are obtained. Particularly, an existence result without using measure of noncompactness condition is presented in ordered and weakly sequentially complete Banach spaces. These results are very convenient for application. As an example, we study the partial differential equation of parabolic type of fractional order.http://dx.doi.org/10.1155/2013/781404 |
| spellingShingle | Yue Liang Yu Ma Xiaoyan Gao Positive Solutions for the Initial Value Problems of Fractional Evolution Equation Journal of Function Spaces and Applications |
| title | Positive Solutions for the Initial Value Problems of Fractional Evolution Equation |
| title_full | Positive Solutions for the Initial Value Problems of Fractional Evolution Equation |
| title_fullStr | Positive Solutions for the Initial Value Problems of Fractional Evolution Equation |
| title_full_unstemmed | Positive Solutions for the Initial Value Problems of Fractional Evolution Equation |
| title_short | Positive Solutions for the Initial Value Problems of Fractional Evolution Equation |
| title_sort | positive solutions for the initial value problems of fractional evolution equation |
| url | http://dx.doi.org/10.1155/2013/781404 |
| work_keys_str_mv | AT yueliang positivesolutionsfortheinitialvalueproblemsoffractionalevolutionequation AT yuma positivesolutionsfortheinitialvalueproblemsoffractionalevolutionequation AT xiaoyangao positivesolutionsfortheinitialvalueproblemsoffractionalevolutionequation |