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Research Article | Open Access

Discontinuous solutions of delay fractional integral equation via measures of noncompactness

Mohamed M. A. Metwali1( ), Shami A. M. Alsallami2
Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt
Department of Mathematical Sciences, College of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia
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Abstract

This article considers the existence and the uniqueness of monotonic solutions of a delay functional integral equation of fractional order in the weighted Lebesgue space L 1 N ( R + ). Our analysis uses a suitable measure of noncompactness, a modified version of Darbo's fixed point theorem, and fractional calculus in the mentioned space. An illustrated example to show the applicability and significance of our outcomes is included.

Keywords

weighted Lebesgue spacedelay fractional integral equationsmeasure of noncompactness (M.N.C.)Carathéodory conditions
CLC number: 47N20, 47H30, 45G10

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AIMS Mathematics
Volume 8 Issue 9,
September 2023
Pages 21055-21068
DOI: 10.3934/math.20231072

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Cite this article:
Metwali MMA, Alsallami SAM. Discontinuous solutions of delay fractional integral equation via measures of noncompactness. AIMS Mathematics, 2023, 8(9): 21055-21068. https://doi.org/10.3934/math.20231072

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Received: 23 February 2023
Revised: 18 April 2023
Accepted: 01 July 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)