Mild solutions for conformable fractional order functional evolution equations via Meir-Keeler type fixed point theorem

被引：0

作者：

Berrighi, Fatma ^{[1
]}

Medjadj, Imene ^{[1
,2
]}

Karapinar, Erdal ^{[3
,4
]}

机构：

[1] Univ Sci & Technol Mohamed Boudiaf USTO MB Mnaouar, Dept Math, BP 1505, Bir El Djir 31000, Oran, Algeria

[2] Univ Oran 1 Ahmed Ben Bella, Lab Fundamental & Appl Math Oran LMFAO, BP 1524, El Mnaouar 31000, Oran, Algeria

[3] Atilim Univ, Dept Math, TR-06830 Incek, Ankara, Turkiye

[4] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan

来源：

FILOMAT | 2025年 / 39卷 / 06期

关键词：

Functional differential equation; mild solution; finite delay; fixed point; condensing operator; measure of noncompactness; conformable fractional; DIFFERENTIAL-EQUATIONS;

D O I：

10.2298/FIL2506989B

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1989 / 2002

页数：14

共 50 条

[1]

Abbas S., 2024, Fractional Difference, Differential Equations, and Inclusions: Analysis and Stability, DOI [10.1016/C2023-0-00030-9, DOI 10.1016/C2023-0-00030-9]

[2] On conformable fractional calculus [J].