Browsing by Author "Sivaranjani Ramasamy"

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    Existence, uniqueness and controllability results of nonlinear neutral implicit ABC fractional integro-differential equations with delay and impulses
    (American Institute of Mathematical Sciences, 2025) Sivaranjani Ramasamy; Thangavelu Senthilprabu; Kulandhaivel Karthikeyan; Palanisamy Geetha; Saowaluck Chasreechai; Thanin Sitthiwirattham; S. Ramasamy; Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore, Tamilnadu, 641 407, India; email: sivaranjanirphd@gmail.com; S. Chasreechai; Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand; email: saowaluck.c@sci.kmutnb.ac.th
    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.