Forecasting and dynamical modeling of reversible enzymatic reactions with a hybrid proportional fractional derivative
Chemical kinetics is a branch of chemistry that investigates the rates of chemical reactions and has applications in cosmology, geology, and physiology. In this study, we develop a mathematical model for chemical reactions based on enzyme dynamics and kinetics, which is a two-step substrate–enzyme r...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2024-01-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2023.1307307/full |
| _version_ | 1797340326143197184 |
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| author | Parvaiz Ahmad Naik Anum Zehra Muhammad Farman Muhammad Farman Aamir Shehzad Sundas Shahzeen Zhengxin Huang |
| author_facet | Parvaiz Ahmad Naik Anum Zehra Muhammad Farman Muhammad Farman Aamir Shehzad Sundas Shahzeen Zhengxin Huang |
| author_sort | Parvaiz Ahmad Naik |
| collection | DOAJ |
| description | Chemical kinetics is a branch of chemistry that investigates the rates of chemical reactions and has applications in cosmology, geology, and physiology. In this study, we develop a mathematical model for chemical reactions based on enzyme dynamics and kinetics, which is a two-step substrate–enzyme reversible reaction, applying chemical kinetics-based modeling of enzyme functions. The non-linear differential equations are transformed into fractional-order systems utilizing the constant proportional Caputo–Fabrizio (CPCF) and constant proportional Atangana–Baleanu–Caputo (CPABC) operators. The system of fractional differential equations is simulated using the Laplace–Adomian decomposition method at different fractional orders through simulations and numerical results. Both qualitative and quantitative analyses such as boundedness, positivity, unique solution, and feasible concentration for the proposed model with different hybrid operators are provided. The stability analysis of the proposed scheme is also verified using Picard’s stable condition through the fixed point theorem. |
| first_indexed | 2024-03-08T10:01:27Z |
| format | Article |
| id | doaj.art-0bba55fcc6644d0a8bf916df30496cf3 |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-03-08T10:01:27Z |
| publishDate | 2024-01-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-0bba55fcc6644d0a8bf916df30496cf32024-01-29T10:10:25ZengFrontiers Media S.A.Frontiers in Physics2296-424X2024-01-011110.3389/fphy.2023.13073071307307Forecasting and dynamical modeling of reversible enzymatic reactions with a hybrid proportional fractional derivativeParvaiz Ahmad Naik0Anum Zehra1Muhammad Farman2Muhammad Farman3Aamir Shehzad4Sundas Shahzeen5Zhengxin Huang6Department of Mathematics and Computer Science, Youjiang Medical University for Nationalities, Baise, Guangxi, ChinaDepartment of Mathematics, The Women University Multan, Multan, PakistanDepartment of Computer Science and Mathematics, Lebanese American University, Beirut, LebanonDepartment of Mathematics, Faculty of Arts and Science, Near East University, Nicosia, CyprusInstitute of Mathematics, Khawaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, PakistanDepartment of Software Engineering, The University of Lahore, Lahore, PakistanDepartment of Mathematics and Computer Science, Youjiang Medical University for Nationalities, Baise, Guangxi, ChinaChemical kinetics is a branch of chemistry that investigates the rates of chemical reactions and has applications in cosmology, geology, and physiology. In this study, we develop a mathematical model for chemical reactions based on enzyme dynamics and kinetics, which is a two-step substrate–enzyme reversible reaction, applying chemical kinetics-based modeling of enzyme functions. The non-linear differential equations are transformed into fractional-order systems utilizing the constant proportional Caputo–Fabrizio (CPCF) and constant proportional Atangana–Baleanu–Caputo (CPABC) operators. The system of fractional differential equations is simulated using the Laplace–Adomian decomposition method at different fractional orders through simulations and numerical results. Both qualitative and quantitative analyses such as boundedness, positivity, unique solution, and feasible concentration for the proposed model with different hybrid operators are provided. The stability analysis of the proposed scheme is also verified using Picard’s stable condition through the fixed point theorem.https://www.frontiersin.org/articles/10.3389/fphy.2023.1307307/fullhybrid proportional derivativeenzymatic reactionPicard’s stabilitymodelingnumerical simulations |
| spellingShingle | Parvaiz Ahmad Naik Anum Zehra Muhammad Farman Muhammad Farman Aamir Shehzad Sundas Shahzeen Zhengxin Huang Forecasting and dynamical modeling of reversible enzymatic reactions with a hybrid proportional fractional derivative Frontiers in Physics hybrid proportional derivative enzymatic reaction Picard’s stability modeling numerical simulations |
| title | Forecasting and dynamical modeling of reversible enzymatic reactions with a hybrid proportional fractional derivative |
| title_full | Forecasting and dynamical modeling of reversible enzymatic reactions with a hybrid proportional fractional derivative |
| title_fullStr | Forecasting and dynamical modeling of reversible enzymatic reactions with a hybrid proportional fractional derivative |
| title_full_unstemmed | Forecasting and dynamical modeling of reversible enzymatic reactions with a hybrid proportional fractional derivative |
| title_short | Forecasting and dynamical modeling of reversible enzymatic reactions with a hybrid proportional fractional derivative |
| title_sort | forecasting and dynamical modeling of reversible enzymatic reactions with a hybrid proportional fractional derivative |
| topic | hybrid proportional derivative enzymatic reaction Picard’s stability modeling numerical simulations |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2023.1307307/full |
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