Existence results for neutral evolution equations with nonlocal conditions and delay via fractional operator
In this paper, we study the existence of solutions for the neutral evolution equations with nonlocal conditions and delay in α\alpha -norm, which are more general than in many previous publications. We assume that the linear part generates an analytic semigroup and transforms them into suitable inte...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-06-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2022-0044 |
| _version_ | 1797998358049062912 |
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| author | Zhang Xuping Sun Pan |
| author_facet | Zhang Xuping Sun Pan |
| author_sort | Zhang Xuping |
| collection | DOAJ |
| description | In this paper, we study the existence of solutions for the neutral evolution equations with nonlocal conditions and delay in α\alpha -norm, which are more general than in many previous publications. We assume that the linear part generates an analytic semigroup and transforms them into suitable integral equations. By using the Kuratowski measure of noncompactness and fixed-point theory, some existence theorems are established without the assumption of compactness on the associated semigroup. Particularly, our results cover the cases where the nonlinear term FF takes values in different spaces such as Xα{X}_{\alpha }. An example of neutral partial differential system is also given to illustrate the feasibility of our abstract results. |
| first_indexed | 2024-04-11T10:47:25Z |
| format | Article |
| id | doaj.art-36238d10adba4ea5a4fe36cb83dd3bfe |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-04-11T10:47:25Z |
| publishDate | 2022-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-36238d10adba4ea5a4fe36cb83dd3bfe2022-12-22T04:29:00ZengDe GruyterOpen Mathematics2391-54552022-06-0120147849110.1515/math-2022-0044Existence results for neutral evolution equations with nonlocal conditions and delay via fractional operatorZhang Xuping0Sun Pan1Department of Mathematics, Northwest Normal University, Lanzhou, 730070, People’s Republic of ChinaDepartment of Mathematics, Northwest Normal University, Lanzhou, 730070, People’s Republic of ChinaIn this paper, we study the existence of solutions for the neutral evolution equations with nonlocal conditions and delay in α\alpha -norm, which are more general than in many previous publications. We assume that the linear part generates an analytic semigroup and transforms them into suitable integral equations. By using the Kuratowski measure of noncompactness and fixed-point theory, some existence theorems are established without the assumption of compactness on the associated semigroup. Particularly, our results cover the cases where the nonlinear term FF takes values in different spaces such as Xα{X}_{\alpha }. An example of neutral partial differential system is also given to illustrate the feasibility of our abstract results.https://doi.org/10.1515/math-2022-0044neutral evolution equationsnonlocal conditionsnonlocal conditionsdelaymeasure of noncompactnessα-norm34k3035d3535k5547j35 |
| spellingShingle | Zhang Xuping Sun Pan Existence results for neutral evolution equations with nonlocal conditions and delay via fractional operator Open Mathematics neutral evolution equations nonlocal conditions nonlocal conditions delay measure of noncompactness α-norm 34k30 35d35 35k55 47j35 |
| title | Existence results for neutral evolution equations with nonlocal conditions and delay via fractional operator |
| title_full | Existence results for neutral evolution equations with nonlocal conditions and delay via fractional operator |
| title_fullStr | Existence results for neutral evolution equations with nonlocal conditions and delay via fractional operator |
| title_full_unstemmed | Existence results for neutral evolution equations with nonlocal conditions and delay via fractional operator |
| title_short | Existence results for neutral evolution equations with nonlocal conditions and delay via fractional operator |
| title_sort | existence results for neutral evolution equations with nonlocal conditions and delay via fractional operator |
| topic | neutral evolution equations nonlocal conditions nonlocal conditions delay measure of noncompactness α-norm 34k30 35d35 35k55 47j35 |
| url | https://doi.org/10.1515/math-2022-0044 |
| work_keys_str_mv | AT zhangxuping existenceresultsforneutralevolutionequationswithnonlocalconditionsanddelayviafractionaloperator AT sunpan existenceresultsforneutralevolutionequationswithnonlocalconditionsanddelayviafractionaloperator |