Existence, uniqueness and controllability results of nonlinear neutral implicit ABC fractional integro-differential equations with delay and impulses
Date
2025
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Article
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American Institute of Mathematical Sciences
Journal Title
Existence, uniqueness and controllability results of nonlinear neutral implicit ABC fractional integro-differential equations with delay and impulses
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Abstract
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 < α < 1 in the sense of 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 Arzelà–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. © 2025 the Author(s), licensee AIMS Press.
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AIMS Mathematics