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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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025200 |
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| Summary: | 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. |
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| ISSN: | 2473-6988 |