Globally analysis of production of lactic acid by Lactobacillus plantarumAC11S: kinetics using Mittag-Leffler kernel via mathematical modeling

In this article, it is investigated how Lactobacillus plantarumAC11S produced lactic acid from lactose. The ideal pH and temperature were established, and the impact of the starting substrate concentration was examined during the formulation of the fractional order mathematical model with Mittag-Leffler kernel global properties. The development of an unstructured mathematical model included formulas for the growth, consumption, and production of products by the bacteria. Different variables were included in the model's solution to account for substrate and/or product inhibition at different growth rates at 30 degrees\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<^>{\circ }$$\end{document}C and pH 6.5 produced the most amounts of lactic acid and promoted the fastest growth of bacteria. An analysis was conducted on the developed model to verify key properties like boundedness, positivity, and the existence of unique solutions with global derivatives. The stability of the model is presented locally as well as global stability including the rate of change of each parameter effects under positive conditions. Solutions are derived using fractional operators for continuous monitoring including its simulation shows the actual states concerning time. Finally, using a two-step Newton polynomial technique, numerical simulations of the effects of various parameters on compartments are used to explore the impact of the fractional operator on different conditions and cases. It is observed from the simulation that the set of equations comprising bacterial growth, substrate consumption, and product production at different beginning substrate concentrations was best characterized by a logistic equation version with a term for product inhibition, even though the modified Gompertz equation matched biomass growth the best. Mainly growth-associated processes produced lactic acid, and significant product inhibition was seen at substrate concentrations greater than 15 g/L. Overall, this study advances our understanding of lactic acid progression and recurrence by establishing a mathematical model that can be used to replicate and evaluate Lactobacillus plantarumAC11S behavior with different factors.