Discontinuous solutions of delay fractional integral equation via measures of noncompactness

Mohamed M. A. Metwali; Shami A. M. Alsallami; Mohamed M. A. Metwali; Shami A. M. Alsallami

doi:10.3934/math.20231072

AIMS Mathematics

2023, Volume 8, Issue 9: 21055-21068. doi: 10.3934/math.20231072

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Research article

Discontinuous solutions of delay fractional integral equation via measures of noncompactness

Mohamed M. A. Metwali ^{1
,
,},
Shami A. M. Alsallami ²

1.
Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt
2.
Department of Mathematical Sciences, College of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia

Received: 23 February 2023 Revised: 18 April 2023 Accepted: 01 July 2023 Published: 03 July 2023
MSC : 47N20, 47H30, 45G10

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({\mathbb{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.
- weighted Lebesgue space,
- delay fractional integral equations,
- measure of noncompactness (M.N.C.),
- Carathéodory conditions
Citation: Mohamed M. A. Metwali, Shami A. M. Alsallami. Discontinuous solutions of delay fractional integral equation via measures of noncompactness[J]. AIMS Mathematics, 2023, 8(9): 21055-21068. doi: 10.3934/math.20231072

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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({\mathbb{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.

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