Solvability of product of $ n $-quadratic Hadamard-type fractional integral equations in Orlicz spaces

Saud Fahad Aldosary; Mohamed M. A. Metwali; Saud Fahad Aldosary; Mohamed M. A. Metwali

doi:10.3934/math.2024541

AIMS Mathematics

2024, Volume 9, Issue 5: 11039-11050. doi: 10.3934/math.2024541

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Solvability of product of $ n $-quadratic Hadamard-type fractional integral equations in Orlicz spaces

Saud Fahad Aldosary ^{1
,
,},
Mohamed M. A. Metwali ²

1.
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia
2.
Department of Mathematics and Computer Science, Faculty of Science, Damanhour University, Damanhour, Egypt

Received: 19 January 2024 Revised: 07 March 2024 Accepted: 12 March 2024 Published: 20 March 2024
MSC : 45G10, 46E30, 47H30, 47N20

The current study demonstrated and studied the existence of monotonic solutions, as well as the uniqueness of the solutions for a general and abstract form of a product of $ n $-quadratic fractional integral equations of Hadamard-type in Orlicz spaces $ L_\varphi $. We utilized the analysis of the measure of non-compactness associated with Darbo's fixed-point theorem and fractional calculus to obtain the results.
Citation: Saud Fahad Aldosary, Mohamed M. A. Metwali. Solvability of product of $ n $-quadratic Hadamard-type fractional integral equations in Orlicz spaces[J]. AIMS Mathematics, 2024, 9(5): 11039-11050. doi: 10.3934/math.2024541

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Abstract

The current study demonstrated and studied the existence of monotonic solutions, as well as the uniqueness of the solutions for a general and abstract form of a product of $ n $-quadratic fractional integral equations of Hadamard-type in Orlicz spaces $ L_\varphi $. We utilized the analysis of the measure of non-compactness associated with Darbo's fixed-point theorem and fractional calculus to obtain the results.

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