New Gronwall-Bellman Type Inequalities and Applications in the Analysis for Solutions to Fractional Differential Equations
Some new Gronwall-Bellman type inequalities are presented in this paper. Based on these inequalities, new explicit bounds for the related unknown functions are derived. The inequalities established can also be used as a handy tool in the research of qualitative as well as quantitative analysis for s...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/705126 |
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| _version_ | 1832567344432414720 |
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| author | Bin Zheng Qinghua Feng |
| author_facet | Bin Zheng Qinghua Feng |
| author_sort | Bin Zheng |
| collection | DOAJ |
| description | Some new Gronwall-Bellman type inequalities are presented in this paper. Based on these inequalities, new explicit bounds for the related unknown functions are derived. The inequalities established can also be used as a handy tool in the research of qualitative as well as quantitative analysis for solutions to some fractional differential equations defined in the sense of the modified Riemann-Liouville fractional derivative. For illustrating the validity of the results established, we present some applications for them, in which the boundedness, uniqueness, and continuous dependence on the initial value for the solutions to some certain
fractional differential and integral equations are investigated. |
| format | Article |
| id | doaj-art-ec57994c5b944d22b18c9f3c80268de7 |
| 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-ec57994c5b944d22b18c9f3c80268de72025-02-03T01:01:46ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/705126705126New Gronwall-Bellman Type Inequalities and Applications in the Analysis for Solutions to Fractional Differential EquationsBin Zheng0Qinghua Feng1School of Science, Shandong University of Technology, Zibo, Shandong 255049, ChinaSchool of Science, Shandong University of Technology, Zibo, Shandong 255049, ChinaSome new Gronwall-Bellman type inequalities are presented in this paper. Based on these inequalities, new explicit bounds for the related unknown functions are derived. The inequalities established can also be used as a handy tool in the research of qualitative as well as quantitative analysis for solutions to some fractional differential equations defined in the sense of the modified Riemann-Liouville fractional derivative. For illustrating the validity of the results established, we present some applications for them, in which the boundedness, uniqueness, and continuous dependence on the initial value for the solutions to some certain fractional differential and integral equations are investigated.http://dx.doi.org/10.1155/2013/705126 |
| spellingShingle | Bin Zheng Qinghua Feng New Gronwall-Bellman Type Inequalities and Applications in the Analysis for Solutions to Fractional Differential Equations Abstract and Applied Analysis |
| title | New Gronwall-Bellman Type Inequalities and Applications in the Analysis for Solutions to Fractional Differential Equations |
| title_full | New Gronwall-Bellman Type Inequalities and Applications in the Analysis for Solutions to Fractional Differential Equations |
| title_fullStr | New Gronwall-Bellman Type Inequalities and Applications in the Analysis for Solutions to Fractional Differential Equations |
| title_full_unstemmed | New Gronwall-Bellman Type Inequalities and Applications in the Analysis for Solutions to Fractional Differential Equations |
| title_short | New Gronwall-Bellman Type Inequalities and Applications in the Analysis for Solutions to Fractional Differential Equations |
| title_sort | new gronwall bellman type inequalities and applications in the analysis for solutions to fractional differential equations |
| url | http://dx.doi.org/10.1155/2013/705126 |
| work_keys_str_mv | AT binzheng newgronwallbellmantypeinequalitiesandapplicationsintheanalysisforsolutionstofractionaldifferentialequations AT qinghuafeng newgronwallbellmantypeinequalitiesandapplicationsintheanalysisforsolutionstofractionaldifferentialequations |