Analysis of an Abstract Delayed Fractional Integro-Differential System via the <i>α</i>-Resolvent Operator

Analysis of an Abstract Delayed Fractional Integro-Differential System via the <i>α</i>-Resolvent Operator

This paper explores the mild solutions of partial impulsive fractional integro-differential systems of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo>&...

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Bibliographic Details
Main Authors:	Ishfaq Khan, Akbar Zada, Ioan-Lucian Popa, Afef Kallekh
Format:	Article
Language:	English
Published:	MDPI AG 2025-02-01
Series:	Axioms
Subjects:	integro-differential system fractional impulse delay stability in terms of Ulam <i>α</i>-resolvent operator
Online Access:	https://www.mdpi.com/2075-1680/14/2/111
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Summary:	This paper explores the mild solutions of partial impulsive fractional integro-differential systems of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>α</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula> in a Banach space. We derive the solution of the system under the assumption that the homogeneous part of the system admits an <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-resolvent operator. Krasnoselskii’s fixed point theorem is used for the existence of solution, while uniqueness is ensured using Banach’s fixed point theorem. The stability of the system is analyzed through the framework of Hyers–Ulam stability using Lipschitz conditions. Finally, examples are presented to illustrate the applicability of the theoretical results.
ISSN:	2075-1680