Mild Solutions for Neutral Conformable Fractional Order Functional Evolution Equations Using Meir-Keeler Type Fixed Point Theorem

Abstract

Our mission is to demonstrate the existence, uniqueness, attractiveness, and controllability of mild solutions to neutral conformable fractional-order functional evolution equations, specifically of order between 1 and 2. These intriguing equations encompass finite delay, all while adhering to local conditions within a separable Banach space. By invoking Meir-Keeler’s fixed-point Theorem and enhancing it with measures of noncompactness, we establish the existence of these solutions. To highlight the potency of our approach, we present a captivating example. © 2025, Politechnica University of Bucharest. All rights reserved.