On Numerical Analysis of Bio-Ethanol Production Model with the Effect of Recycling and Death Rates under Fractal Fractional Operators with Three Different Kernels

Abstract

The main metabolism of yeasts produces bioethanol. Bioethanol, which is produced from biomass and bioenergy crops, has been promoted as one of the most viable alternatives to fossil fuels. The following reaction represents all of the knowledge we have regarding intracellular reactions and their regulatory mechanisms: biomass+substrates→ethanol+biomass(morecells). Atangana has suggested new operators based on a combination of fractional and fractal calculus. Fractal-fractional operators (FFOs) have frequently been utilized to investigate the dynamics of a physical problem. In this paper, FFOs are used to investigate a nonlinear mathematical model for ethanol production with three different kernels. Famous fixed point results are employed to show the existence and uniqueness of the solution of the FFO ethanol model under the Mittag–Leffler kernel. The concept of non-linear analysis is utilized to demonstrate the model’s Ulam–Hyres stability. The Adams—Bashforth numerical technique, which is based on the Lagrangian interpolation method, is utilized to find the solution of the model under fractal-fractional operators with three different kernels. The numerical results are simulated with MATLAB-17 for several sets of fractional orders and fractal dimensions to show the relationship between components of ethanol production under new operators in various senses.