Applications of artificial intelligence to analyze chain reaction of Uranium illustrated by discrete Caputo's fractional mathematical model

Volume 39, Issue 2, pp 263--279 https://dx.doi.org/10.22436/jmcs.039.02.06

Publication Date: March 29, 2025 Submission Date: November 11, 2024 Revision Date: January 07, 2025 Accteptance Date: February 13, 2025

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Authors

H. Khan - Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia. - Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Dir Upper, Khyber Pakhtunkhwa, Pakistan. J. Alzabut - Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia. - Department of Industrial Engineering, OSTIM Technical University, 06374 Ankara, Türkiye. W. Kh. Alqurashi - Department of Mathematics, Faculty of Science, Umm Al-Qura University, Makkah, Saudi Arabia. D. K. Almutairi - Department of Mathematics, College of Science Al-Zulfi, Majmaah University, 11952 Al-Majmaah, Saudi Arabia.

Abstract

This paper presents an investigation into the alpha decay chain reactions of Uranium-238 (\(\mathcal{N}_{U_ {238}}\)) into Thorium-234 \(\mathcal{N}_{Th_{234}}\) and Radium-226 \(\mathcal{N}_{Ra_{226}}\) with the help of a fractional -order Caputo difference model. This study explores the effects of changing the initial amount of Uranium-238 and distinct decay constants on the final populations of decay products. Through a sophisticated computational scheme, the results show that a larger amount of uranium-238 leads to increased production of thorium-234 and radium-226, with the decay constants exerting significant control over the system's temporal evolution. The existence and stability of the solutions are confirmed via a fixed-point approach, establishing convergence toward steady-state conditions. Furthermore, the integration of artificial intelligence (AI) techniques is applied to further analyze uranium decay and increase computational efficiency. The AI-driven approach provides good analysis of parameter sensitivity and prediction accuracy, enabling a more refined understanding of radioactive decay dynamics. This work lays a foundation for the development of more useful computational models within the domain of nuclear science.

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Keywords

• Uranium decay analysis
• modeling with discrete Caputo's difference
• qualitative results for the dynamics
• computational results
• artificial intelligence

MSC

•  34A08
•  34A09
•  34A34

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