Controllability of a fuzzy solution for nonlinear second order functional neutral integro-differential equations

Abstract

 In this paper, we focus on the controllability of fuzzy solutions for a specific class of nonlinear second-order functional neutral integrodifferential equations. To tackle this problem, we employ the Banach fixed-point theorem, a fundamental result in functional analysis that is particularly useful for demonstrating the existence and uniqueness of solutions under certain conditions.

 Our study revolves around fuzzy numbers, which are a type of mathematical representation used to handle uncertainty and imprecision. Specifically, we consider fuzzy numbers that are normal, convex, upper semicontinuous, and have compactly supported intervals. These properties ensure that the fuzzy numbers are well-behaved and manageable within our theoretical framework.

To illustrate the practical application of our theoretical results, we provide an example. This example demonstrates how the conditions and methods developed in the paper can be used to analyze and solve a specific instance of the nonlinear second-order functional neutral integrodifferential equation. By applying our findings, we can verify the controllability of the fuzzy solution in this particular case, thereby validating the theoretical framework and its utility in real-world scenarios.