Existence, uniqueness and controllability results of nonlinear neutral implicit $ \mathcal{ABC} $ fractional integro-differential equations with delay and impulses
In this article, the necessary and sufficient conditions for the existence and uniqueness of the mild solutions for nonlinear neutral implicit integro-differential equations of non-integer order $ 0 < \alpha < 1 $ in the sense of $ \mathcal{ABC} $ derivative with impulses, delay, and integro i...
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AIMS Press
2025-02-01
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025200 |
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| author | Sivaranjani Ramasamy Thangavelu Senthilprabu Kulandhaivel Karthikeyan Palanisamy Geetha Saowaluck Chasreechai Thanin Sitthiwirattham |
| author_facet | Sivaranjani Ramasamy Thangavelu Senthilprabu Kulandhaivel Karthikeyan Palanisamy Geetha Saowaluck Chasreechai Thanin Sitthiwirattham |
| author_sort | Sivaranjani Ramasamy |
| collection | DOAJ |
| description | In this article, the necessary and sufficient conditions for the existence and uniqueness of the mild solutions for nonlinear neutral implicit integro-differential equations of non-integer order $ 0 < \alpha < 1 $ in the sense of $ \mathcal{ABC} $ derivative with impulses, delay, and integro initial conditions were established. The existence results were derived using the semi-group theory, measures of non-compactness, and the fixed-point theory in the sense of Arzel$ \grave{a} $–Ascoli theorem and Schauder's fixed-point theorem. We analyzed the controllability results of the proposed problem by incorporating the ideas of semi-group theory and fixed-point techniques. The Banach contraction principle was used to derive the uniqueness and controllability of the proposed problem. We provide an example to support the theoretical results. |
| format | Article |
| id | doaj-art-7e841b6074aa4074afc8b37a0bad16bf |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-7e841b6074aa4074afc8b37a0bad16bf2025-08-20T01:54:41ZengAIMS PressAIMS Mathematics2473-69882025-02-011024326435410.3934/math.2025200Existence, uniqueness and controllability results of nonlinear neutral implicit $ \mathcal{ABC} $ fractional integro-differential equations with delay and impulsesSivaranjani Ramasamy0Thangavelu Senthilprabu1Kulandhaivel Karthikeyan2Palanisamy Geetha3Saowaluck Chasreechai4Thanin Sitthiwirattham5Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore 641 407, Tamilnadu, IndiaDepartment of Mathematics, KPR Institute of Engineering and Technology, Coimbatore 641 407, Tamilnadu, IndiaDepartment of Mathematics, KPR Institute of Engineering and Technology, Coimbatore 641 407, Tamilnadu, IndiaDepartment of Mathematics, KPR College of Arts Science and Research, Coimbatore 641 407, Tamilnadu, IndiaDepartment of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, ThailandResearch Group for Fractional Calculus Theory and Applications, Science and Technology Research Institute, King Mongkut's University of Technology North Bangkok, Bangkok 10800, ThailandIn this article, the necessary and sufficient conditions for the existence and uniqueness of the mild solutions for nonlinear neutral implicit integro-differential equations of non-integer order $ 0 < \alpha < 1 $ in the sense of $ \mathcal{ABC} $ derivative with impulses, delay, and integro initial conditions were established. The existence results were derived using the semi-group theory, measures of non-compactness, and the fixed-point theory in the sense of Arzel$ \grave{a} $–Ascoli theorem and Schauder's fixed-point theorem. We analyzed the controllability results of the proposed problem by incorporating the ideas of semi-group theory and fixed-point techniques. The Banach contraction principle was used to derive the uniqueness and controllability of the proposed problem. We provide an example to support the theoretical results.https://www.aimspress.com/article/doi/10.3934/math.2025200fractional derivativeimplicit neutral differential equationscontrollabilitysemi-group and fixed point theories |
| spellingShingle | Sivaranjani Ramasamy Thangavelu Senthilprabu Kulandhaivel Karthikeyan Palanisamy Geetha Saowaluck Chasreechai Thanin Sitthiwirattham Existence, uniqueness and controllability results of nonlinear neutral implicit $ \mathcal{ABC} $ fractional integro-differential equations with delay and impulses AIMS Mathematics fractional derivative implicit neutral differential equations controllability semi-group and fixed point theories |
| title | Existence, uniqueness and controllability results of nonlinear neutral implicit $ \mathcal{ABC} $ fractional integro-differential equations with delay and impulses |
| title_full | Existence, uniqueness and controllability results of nonlinear neutral implicit $ \mathcal{ABC} $ fractional integro-differential equations with delay and impulses |
| title_fullStr | Existence, uniqueness and controllability results of nonlinear neutral implicit $ \mathcal{ABC} $ fractional integro-differential equations with delay and impulses |
| title_full_unstemmed | Existence, uniqueness and controllability results of nonlinear neutral implicit $ \mathcal{ABC} $ fractional integro-differential equations with delay and impulses |
| title_short | Existence, uniqueness and controllability results of nonlinear neutral implicit $ \mathcal{ABC} $ fractional integro-differential equations with delay and impulses |
| title_sort | existence uniqueness and controllability results of nonlinear neutral implicit mathcal abc fractional integro differential equations with delay and impulses |
| topic | fractional derivative implicit neutral differential equations controllability semi-group and fixed point theories |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025200 |
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