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

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.