Fractal Fractional Derivative Models for Simulating Chemical Degradation in a Bioreactor

A three-differential-equation mathematical model is presented for the degradation of phenol and p-cresol combination in a bioreactor that is continually agitated. The stability analysis of the model’s equilibrium points, as established by the study, is covered. Additionally, we used three alternativ...

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Bibliographic Details
Published inAxioms Vol. 13; no. 3; p. 151
Main Authors Akgül, Ali, Conejero, J. Alberto
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.02.2024
Subjects
Bacteria
bioreactor model
Bioreactors
Decomposition (Chemistry)
Degradation
Differential equations
Fractal analysis
Fractal models
Fractals
fractal–fractional derivatives
Mathematical models
Membrane reactors
numerical methods
numerical simulations
Simulation
Stability analysis
Water treatment
Turkey
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Summary:A three-differential-equation mathematical model is presented for the degradation of phenol and p-cresol combination in a bioreactor that is continually agitated. The stability analysis of the model’s equilibrium points, as established by the study, is covered. Additionally, we used three alternative kernels to analyze the model with the fractal–fractional derivatives, and we looked into the effects of the fractal size and fractional order. We have developed highly efficient numerical techniques for the concentration of biomass, phenol, and p-cresol. Lastly, numerical simulations are used to illustrate the accuracy of the suggested method.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13030151