Existence, uniqueness, continuous dependence on the data for the product of $ n $-fractional integral equations in Orlicz spaces

Abdulaziz M. Alotaibi; Mohamed M. A. Metwali; Hala H. Taha; Ravi P Agarwal; Abdulaziz M. Alotaibi; Mohamed M. A. Metwali; Hala H. Taha; Ravi P Agarwal

doi:10.3934/math.2025386

AIMS Mathematics

2025, Volume 10, Issue 4: 8382-8397. doi: 10.3934/math.2025386

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Existence, uniqueness, continuous dependence on the data for the product of $ n $-fractional integral equations in Orlicz spaces

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
3.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
4.
Emeritus Research Professor, Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA

Received: 30 January 2025 Revised: 03 April 2025 Accepted: 08 April 2025 Published: 11 April 2025
MSC : 45G10, 47H10, 47H30, 47N20

In this manuscript, the measure of noncompactness, the fixed-point theorem, as well as fractional calculus, are used to carry out the analysis of the solvability of a product of $ n $-quadratic Erdélyi-Kober ($ \mathbf{\mathcal{EK}} $) fractional-type integral equations in Orlicz spaces $ L_\varphi $. Several qualitative properties of the solution for the studied problem are established, such as the existence, monotonicity, uniqueness, and continuous dependence on the data. We conclude with some examples that illustrate our hypothesis.
Citation: Abdulaziz M. Alotaibi, Mohamed M. A. Metwali, Hala H. Taha, Ravi P Agarwal. Existence, uniqueness, continuous dependence on the data for the product of $ n $-fractional integral equations in Orlicz spaces[J]. AIMS Mathematics, 2025, 10(4): 8382-8397. doi: 10.3934/math.2025386

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Abstract

In this manuscript, the measure of noncompactness, the fixed-point theorem, as well as fractional calculus, are used to carry out the analysis of the solvability of a product of $ n $-quadratic Erdélyi-Kober ($ \mathbf{\mathcal{EK}} $) fractional-type integral equations in Orlicz spaces $ L_\varphi $. Several qualitative properties of the solution for the studied problem are established, such as the existence, monotonicity, uniqueness, and continuous dependence on the data. We conclude with some examples that illustrate our hypothesis.

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