Mild solutions for fractional non-instantaneous impulses integro-differential equations with nonlocal conditions
In this paper, we investigated Caputo fractional integro-differential equations with non-instantaneous impulses and nonlocal conditions. By employing the solution operator, the Mönch fixed point theorem, and the stepwise estimation method, we eliminated the Lipschitz condition of the nonlinear term,...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024589?viewType=HTML |
| _version_ | 1827288949887860736 |
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| author | Ye Li Biao Qu |
| author_facet | Ye Li Biao Qu |
| author_sort | Ye Li |
| collection | DOAJ |
| description | In this paper, we investigated Caputo fractional integro-differential equations with non-instantaneous impulses and nonlocal conditions. By employing the solution operator, the Mönch fixed point theorem, and the stepwise estimation method, we eliminated the Lipschitz condition of the nonlinear term, while also dispensing with the requirement for the compressibility coefficient condition $ 0 < k < 1 $. The main results presented represented a generalization and enhancement of previous findings. Furthermore, an example was provided to verify the application of our main results. |
| first_indexed | 2024-04-24T11:41:25Z |
| format | Article |
| id | doaj.art-329059835cf1488ebf718187baf77184 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-24T11:41:25Z |
| publishDate | 2024-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-329059835cf1488ebf718187baf771842024-04-10T01:20:18ZengAIMS PressAIMS Mathematics2473-69882024-03-0195120571207110.3934/math.2024589Mild solutions for fractional non-instantaneous impulses integro-differential equations with nonlocal conditionsYe Li 0Biao Qu 11. School of Data and Computer Science, Shandong Women's University, China 2. Institute of Operations Research, Qufu Normal University, China2. Institute of Operations Research, Qufu Normal University, ChinaIn this paper, we investigated Caputo fractional integro-differential equations with non-instantaneous impulses and nonlocal conditions. By employing the solution operator, the Mönch fixed point theorem, and the stepwise estimation method, we eliminated the Lipschitz condition of the nonlinear term, while also dispensing with the requirement for the compressibility coefficient condition $ 0 < k < 1 $. The main results presented represented a generalization and enhancement of previous findings. Furthermore, an example was provided to verify the application of our main results. https://www.aimspress.com/article/doi/10.3934/math.2024589?viewType=HTMLfractional integro-differential equationssolution operatornon-instantaneous impulsemeasure of non-compactnessmönch fixed point theorem |
| spellingShingle | Ye Li Biao Qu Mild solutions for fractional non-instantaneous impulses integro-differential equations with nonlocal conditions AIMS Mathematics fractional integro-differential equations solution operator non-instantaneous impulse measure of non-compactness mönch fixed point theorem |
| title | Mild solutions for fractional non-instantaneous impulses integro-differential equations with nonlocal conditions |
| title_full | Mild solutions for fractional non-instantaneous impulses integro-differential equations with nonlocal conditions |
| title_fullStr | Mild solutions for fractional non-instantaneous impulses integro-differential equations with nonlocal conditions |
| title_full_unstemmed | Mild solutions for fractional non-instantaneous impulses integro-differential equations with nonlocal conditions |
| title_short | Mild solutions for fractional non-instantaneous impulses integro-differential equations with nonlocal conditions |
| title_sort | mild solutions for fractional non instantaneous impulses integro differential equations with nonlocal conditions |
| topic | fractional integro-differential equations solution operator non-instantaneous impulse measure of non-compactness mönch fixed point theorem |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024589?viewType=HTML |
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