The Iterative Scheme and the Convergence Analysis of Unique Solution for a Singular Fractional Differential Equation from the Eco-Economic Complex System’s Co-Evolution Process
In this paper, we focus on a class of singular fractional differential equation, which arises from many complex processes such as the phenomenon and diffusion interaction of the ecological-economic-social complex system. By means of the iterative technique, the uniqueness and nonexistence results of...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/9278056 |
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| author | Teng Ren Helu Xiao Zhongbao Zhou Xinguang Zhang Lining Xing Zhongwei Wang Yujun Cui |
| author_facet | Teng Ren Helu Xiao Zhongbao Zhou Xinguang Zhang Lining Xing Zhongwei Wang Yujun Cui |
| author_sort | Teng Ren |
| collection | DOAJ |
| description | In this paper, we focus on a class of singular fractional differential equation, which arises from many complex processes such as the phenomenon and diffusion interaction of the ecological-economic-social complex system. By means of the iterative technique, the uniqueness and nonexistence results of positive solutions are established under the condition concerning the spectral radius of the relevant linear operator. In addition, the iterative scheme that converges to the unique solution is constructed without request of any monotonicity, and the convergence analysis and error estimate of unique solution are obtained. The numerical example and simulation are also given to demonstrate the application of the main results and the effectiveness of iterative process. |
| format | Article |
| id | doaj-art-586bdb4c460b43209c361f8ff5ddb43f |
| institution | OA Journals |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-586bdb4c460b43209c361f8ff5ddb43f2025-08-20T02:05:21ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/92780569278056The Iterative Scheme and the Convergence Analysis of Unique Solution for a Singular Fractional Differential Equation from the Eco-Economic Complex System’s Co-Evolution ProcessTeng Ren0Helu Xiao1Zhongbao Zhou2Xinguang Zhang3Lining Xing4Zhongwei Wang5Yujun Cui6School of Transportation and Logistics, Central South University of Forestry and Technology, Changsha 410018, ChinaBusiness School, Hunan Normal University, Changsha 410081, ChinaSchool of Business Administration, Hunan University, Changsha 410082, ChinaSchool of Mathematical and Informational Sciences, Yantai University, Yantai 264005, Shandong, ChinaSchool of Transportation and Logistics, Central South University of Forestry and Technology, Changsha 410018, ChinaSchool of Transportation and Logistics, Central South University of Forestry and Technology, Changsha 410018, ChinaDepartment of Mathematics, Shandong University of Science and Technology, Qingdao 266590, Shandong, ChinaIn this paper, we focus on a class of singular fractional differential equation, which arises from many complex processes such as the phenomenon and diffusion interaction of the ecological-economic-social complex system. By means of the iterative technique, the uniqueness and nonexistence results of positive solutions are established under the condition concerning the spectral radius of the relevant linear operator. In addition, the iterative scheme that converges to the unique solution is constructed without request of any monotonicity, and the convergence analysis and error estimate of unique solution are obtained. The numerical example and simulation are also given to demonstrate the application of the main results and the effectiveness of iterative process.http://dx.doi.org/10.1155/2019/9278056 |
| spellingShingle | Teng Ren Helu Xiao Zhongbao Zhou Xinguang Zhang Lining Xing Zhongwei Wang Yujun Cui The Iterative Scheme and the Convergence Analysis of Unique Solution for a Singular Fractional Differential Equation from the Eco-Economic Complex System’s Co-Evolution Process Complexity |
| title | The Iterative Scheme and the Convergence Analysis of Unique Solution for a Singular Fractional Differential Equation from the Eco-Economic Complex System’s Co-Evolution Process |
| title_full | The Iterative Scheme and the Convergence Analysis of Unique Solution for a Singular Fractional Differential Equation from the Eco-Economic Complex System’s Co-Evolution Process |
| title_fullStr | The Iterative Scheme and the Convergence Analysis of Unique Solution for a Singular Fractional Differential Equation from the Eco-Economic Complex System’s Co-Evolution Process |
| title_full_unstemmed | The Iterative Scheme and the Convergence Analysis of Unique Solution for a Singular Fractional Differential Equation from the Eco-Economic Complex System’s Co-Evolution Process |
| title_short | The Iterative Scheme and the Convergence Analysis of Unique Solution for a Singular Fractional Differential Equation from the Eco-Economic Complex System’s Co-Evolution Process |
| title_sort | iterative scheme and the convergence analysis of unique solution for a singular fractional differential equation from the eco economic complex system s co evolution process |
| url | http://dx.doi.org/10.1155/2019/9278056 |
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