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Citation - WoS: 5
Citation - Scopus: 5
Mild Solutions for Conformable Fractional Order Functional Evolution Equations Via Meir-Keeler Type Fixed Point Theorem
(Univ Nis, Fac Sci Math, 2025) Berrighi, Fatma; Medjadj, Imene; Karapinar, Erdal
In this study, we delve into the realm of mild solutions for conformable fractional order functional evolution equations, focusing on cases where the fractional order is strictly greater than 1 and less than 2 within a separable Banach space. We demonstrate the existence, uniqueness, attractivity, and controllability of these solutions under local conditions. Our approach involves leveraging a contribution of Meir-Keeler's fixed point theorem alongside the principle of measures of noncompactness. To demonstrate the practical ramifications of our theoretical finds, we provide a specific example that underscores the relevance and applications of the established results.
Citation - WoS: 6
Citation - Scopus: 9
On Interpolative Metric Spaces
(Univ Nis, Fac Sci Math, 2024) Karapinar, Erdal
The purpose of this article is to expand the "open discussion" on the definition and necessity of the interpolation metric space and keep it on the agenda of researchers in nonlinear functional analysis. The secondary aim of this article is to indicate that the outcomes of this "open discussion" have the potential to stop the recent recession in the metric fixed point theory.