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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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/13/3/151 |
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| author | Ali Akgül J. Alberto Conejero |
| author_facet | Ali Akgül J. Alberto Conejero |
| author_sort | Ali Akgül |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T18:33:28Z |
| format | Article |
| id | doaj.art-7b9091cb5e7c4851a5924bb293c8ddc2 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-04-24T18:33:28Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-7b9091cb5e7c4851a5924bb293c8ddc22024-03-27T13:20:58ZengMDPI AGAxioms2075-16802024-02-0113315110.3390/axioms13030151Fractal Fractional Derivative Models for Simulating Chemical Degradation in a BioreactorAli Akgül0J. Alberto Conejero1Department of Mathematics, Art and Science Faculty, Siirt University, 56100 Siirt, TurkeyInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 València, SpainA 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.https://www.mdpi.com/2075-1680/13/3/151bioreactor modelnumerical methodsfractal–fractional derivativesnumerical simulations |
| spellingShingle | Ali Akgül J. Alberto Conejero Fractal Fractional Derivative Models for Simulating Chemical Degradation in a Bioreactor Axioms bioreactor model numerical methods fractal–fractional derivatives numerical simulations |
| title | Fractal Fractional Derivative Models for Simulating Chemical Degradation in a Bioreactor |
| title_full | Fractal Fractional Derivative Models for Simulating Chemical Degradation in a Bioreactor |
| title_fullStr | Fractal Fractional Derivative Models for Simulating Chemical Degradation in a Bioreactor |
| title_full_unstemmed | Fractal Fractional Derivative Models for Simulating Chemical Degradation in a Bioreactor |
| title_short | Fractal Fractional Derivative Models for Simulating Chemical Degradation in a Bioreactor |
| title_sort | fractal fractional derivative models for simulating chemical degradation in a bioreactor |
| topic | bioreactor model numerical methods fractal–fractional derivatives numerical simulations |
| url | https://www.mdpi.com/2075-1680/13/3/151 |
| work_keys_str_mv | AT aliakgul fractalfractionalderivativemodelsforsimulatingchemicaldegradationinabioreactor AT jalbertoconejero fractalfractionalderivativemodelsforsimulatingchemicaldegradationinabioreactor |