Modeling and Ulam-Hyers stability analysis of oleic acid epoxidation by using a fractional-order kinetic model

Abstract

Government initiatives, price cuts, and innovations in technology have caused a shift in the world's raw material consumption towards renewable materials. The polymer industry has shown particular interest in studies on more environmentally friendly epoxidation processes that use vegetable oils. Epoxidized vegetable oils are renewable, affordable, and eco-friendly, which makes them a promising green material to partially replace and toughen polymers derived from petrochemicals. Using a kinetic model from the literature, this study develops a system of fractional-order differential equations to investigate the significance of oleic acid epoxidation. With oleic acid serving as the primary raw material, the study focuses on producing epoxidized oleic acid with a high yield and a longer reaction time. We apply both qualitative and quantitative analysis to the model using fixed-point theorems. The model's Ulam-Hyers stability is established. Investigation of the fractional operator's effect is done through computational simulations and the Laplace Adomian decomposition technique. The investigation of the effects of fractional operators on the epoxidation process reveals that temperature, molar ratios, and fractional order are significant determinants of the process.