Weighted fractional differential equations with infinite delay in Banach spaces
This paper is devoted to the study of fractional differential equations with Riemann-Liouville fractional derivatives and infinite delay in Banach spaces. The weighted delay is developed to deal with the case of non-zero initial value, which leads to the unboundedness of the solutions. Existence and...
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De Gruyter
2016-01-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2016-0035 |
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doaj-d2f874544be74c14b5fe4be4dbe09bd02021-09-06T19:20:07ZengDe GruyterOpen Mathematics2391-54552016-01-0114137038310.1515/math-2016-0035math-2016-0035Weighted fractional differential equations with infinite delay in Banach spacesDong Qixiang0Liu CanFan ZhenbinSchool of Mathematical Sciences, Yangzhou University, Yangzhou 225002, P.R. ChinaThis paper is devoted to the study of fractional differential equations with Riemann-Liouville fractional derivatives and infinite delay in Banach spaces. The weighted delay is developed to deal with the case of non-zero initial value, which leads to the unboundedness of the solutions. Existence and uniqueness results are obtained based on the theory of measure of non-compactness, Schaude’s and Banach’s fixed point theorems. As auxiliary results, a fractional Gronwall type inequality is proved, and the comparison property of fractional integral is discussed.https://doi.org/10.1515/math-2016-0035fractional integralfractional derivativefunctional differential equationinfinite delay34a0834k37 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Dong Qixiang Liu Can Fan Zhenbin |
| spellingShingle |
Dong Qixiang Liu Can Fan Zhenbin Weighted fractional differential equations with infinite delay in Banach spaces Open Mathematics fractional integral fractional derivative functional differential equation infinite delay 34a08 34k37 |
| author_facet |
Dong Qixiang Liu Can Fan Zhenbin |
| author_sort |
Dong Qixiang |
| title |
Weighted fractional differential equations with infinite delay in Banach spaces |
| title_short |
Weighted fractional differential equations with infinite delay in Banach spaces |
| title_full |
Weighted fractional differential equations with infinite delay in Banach spaces |
| title_fullStr |
Weighted fractional differential equations with infinite delay in Banach spaces |
| title_full_unstemmed |
Weighted fractional differential equations with infinite delay in Banach spaces |
| title_sort |
weighted fractional differential equations with infinite delay in banach spaces |
| publisher |
De Gruyter |
| series |
Open Mathematics |
| issn |
2391-5455 |
| publishDate |
2016-01-01 |
| description |
This paper is devoted to the study of fractional differential equations with Riemann-Liouville fractional derivatives and infinite delay in Banach spaces. The weighted delay is developed to deal with the case of non-zero initial value, which leads to the unboundedness of the solutions. Existence and uniqueness results are obtained based on the theory of measure of non-compactness, Schaude’s and Banach’s fixed point theorems. As auxiliary results, a fractional Gronwall type inequality is proved, and the comparison property of fractional integral is discussed. |
| topic |
fractional integral fractional derivative functional differential equation infinite delay 34a08 34k37 |
| url |
https://doi.org/10.1515/math-2016-0035 |
| work_keys_str_mv |
AT dongqixiang weightedfractionaldifferentialequationswithinfinitedelayinbanachspaces AT liucan weightedfractionaldifferentialequationswithinfinitedelayinbanachspaces AT fanzhenbin weightedfractionaldifferentialequationswithinfinitedelayinbanachspaces |
| _version_ |
1717777332779876352 |