β–Ulam–Hyers Stability and Existence of Solutions for Non-Instantaneous Impulsive Fractional Integral Equations-Reference-Cited by-同舟云学术

β–Ulam–Hyers Stability and Existence of Solutions for Non-Instantaneous Impulsive Fractional Integral Equations

Published:2024-08-12 Issue:8 Volume:8 Page:469
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Du Wei-Shih¹^ORCID,Fečkan Michal²^ORCID,Kostić Marko³^ORCID,Velinov Daniel⁴^ORCID

Affiliation:

1. Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan

2. Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynskaá Dolina, 842 48 Bratislava, Slovakia

3. Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia

4. Department for Mathematics and Informatics, Faculty of Civil Engineering, Ss. Cyril and Methodius University in Skopje, Partizanski Odredi 24, P.O. Box 560, 1000 Skopje, North Macedonia

Abstract

In this paper, we investigate a class of non-instantaneous impulsive fractional integral equations. Utilizing the Banach contraction mapping principle, we establish the existence and uniqueness of solutions for the considered problem. Additionally, employing Schauder’s fixed-point theorem, we demonstrate the existence of solutions within the framework of β-Banach spaces. Moreover, we examine the β–Ulam–Hyers stability of the solutions, providing insights into the stability behavior under small perturbations. An illustrative example is presented to demonstrate the practical applicability and effectiveness of the theoretical results obtained.

Funder

National Science and Technology Council of the Republic of China

Slovak Research and Development Agency

Slovak Grant Agency VEGA

Ministry of Science and Technological Development, Republic of Serbia and Bilateral project between MANU and SANU

Publisher

MDPI AG

Link

https://www.mdpi.com/2504-3110/8/8/469/pdf

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