Green Synthesis of Silver Nanoparticles with \textit{Musa Acuminata} Flower Extraction: A Fractional Approach

Abstract

Green nanotechnology offers sustainable solutions to global issues by producing metal oxide nanoparticles with unique properties through eco-friendly methods. Green synthesis using flower extracts is especially promising, utilizing natural bio-reducing agents for nanoparticle formation and stabilization. In this study, we investigated the activity of silver nanoparticles synthesized with \textit{Musa Acuminata} flower extract through a novel green procedure. The rapid color change due to the addition of the aqueous extract to the silver nitrate solution confirmed the reduction of \(\text{Ag}^+\) ions to \(\text{Ag}\) nanoparticles. The photocatalytic efficiency of these green-synthesized nanoparticles was evaluated under solar radiation for degrading methyl orange, resulting in up to 90\% degradation within 300 minutes. The UV–Vis spectrum verified the formation of nanoparticles, showing an absorbance band at 430 nm. This study extends the experimental findings by applying fractional mathematical modeling, using the Caputo fractional derivative. The Sumudu Decomposition Method (SDM) is employed to obtain numerical solutions for the proposed model. The boundedness, existence, and uniqueness theorems validate the model's reliability. Numerical simulations demonstrate the model's accuracy and consistency with the experimental data, offering valuable insights into the behavior and effectiveness of green-synthesized nanoparticles in real-world applications.