@article{Ramasamy2025, 
author = {Sivaranjani Ramasamy and Thangavelu Senthilprabu and Kulandhaivel Karthikeyan and Palanisamy Geetha and Saowaluck Chasreechai and Thanin Sitthiwirattham},
title = {Existence, uniqueness and controllability results of nonlinear neutral implicit        A    B    C   fractional integro-differential equations with delay and impulses},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {2},
pages = {4326-4354},
keywords = {fractional derivative, implicit neutral differential equations, controllability, semi-group and fixed point theories},
url = {https://www.sciopen.com/article/10.3934/math.2025200},
doi = {10.3934/math.2025200},
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        A    B    C   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             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.}
}