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Article Mild Solutions for Neutral Conformable Fractional Order Functional Evolution Equations Using Meir-Keeler Type Fixed Point Theorem(Politechnica University of Bucharest, 2025) Berrighi, F.; Medjadj, I.; Karapınar, E.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.Article Citation - Scopus: 2On the Novelty of “Contracting Perimeters of Triangles in Metric Space”(Erdal Karapinar, 2025) Karapınar, E.In this note, we investigate whether the newly introduced notion of “contracting perimeters of triangles” in the context of standard metric spaces is novel or equivalent to “a variant” of Banach contraction in the setting of G-metric spaces. By using the fact that G-metric spaces are equivalent to quasi-metric spaces, we reconsider our main question as whether the fixed-point theorems via “contracting perimeters of triangles” is equivalent to a fixed point of the same mapping in the context of quasi-metric spaces. © 2025, Erdal Karapinar. All rights reserved.
