Title: Existence and controllability of non-instantaneous impulsive higher order fuzzy neutral integrodifferential equation

Authors: M. Nagarajan; B. Radhakrishnan; K. Karthik; P. Chandrasekaran

Addresses: Department of Mathematics, Dhaanish Ahmed Institute of Technology, Coimbatore – 641105, India ' Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore – 641407, India ' Department of Mathematics, Christ the King Engineering College, Coimbatore – 641104, India ' Department of Mathematics, Government Arts College, Coimbatore – 641118, India

Abstract: This paper examines whether a solution exists for a specific kind of differential equation: a fuzzy, nonlinear, second-order impulsive functional neutral differential equation with non-instantaneous impulses. We do this by applying the power source Banach fixed point theorem, a key idea in mathematical analysis. The controllability outcomes are also governed by the same system. A fuzzy number with properties such as upper semi-continuity, convexity, normality, and compactly supported intervals is the subject of our study. To illustrate the application and value of our theoretical conclusions, we also provide an instance from reality in the conclusion.

Keywords: second order differential equation; cosine and sine family of operators; neutral differential equation; fuzzy sets; fixed point approach.

DOI: 10.1504/IJDSDE.2025.150092

International Journal of Dynamical Systems and Differential Equations, 2025 Vol.14 No.5, pp.425 - 456

Received: 20 May 2025
Accepted: 03 Sep 2025
Published online: 28 Nov 2025 *

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