Chaos control and production of Lactic Acid by Lactobacillus plantarum AC 11S - Kinetics using Caputo fractional operator: Mathematical Modeling

In this article, it is investigated that how Lactobacillus plantarum AC 11S 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 mathematical model. 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 [Formula: see text]C and [Formula: see text] produced the most amounts of lactic acid and promoted the fastest growth of bacteria. Mainly growth-associated processes produced lactic acid, and significant product inhibition was seen at substrate concentrations greater than 15 g/L. An analysis was conducted on the developed model to verify key properties like existence of unique solutions including positivity and bounded solutions. Equilibrium stage of the model is presented with constant the rate of change to verify the stable state. An analysis was conducted on the developed model using Caputo fractional operator that is iterative and stable. Solutions are derived using fractional operators for continuous monitoring including its simulation show the actual states with respect to time behaves including chaos control of the Lactic acid model. 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.