Multistep generalized transformation method applied to solving equations of discrete and continuous time-fractional enzyme kinetics. (English) Zbl 1466.92070
Summary: In this paper, Caputo based Michaelis-Menten kinetic model based on time scale calculus (TSC) is proposed. The main reason for its consideration is a study of tumor cells population growth dynamics. In the particular case discrete-continuous time kinetics, Michaelis-Menten model is numerically treated, using a new algorithm proposed by authors, called multistep generalized difference transformation method (MSGDETM). In addition numerical simulations are performed and is shown that it represents the upgrade of the multi-step variant of generalized differential transformation method (MSGDTM). A possible conditions for its further development are discussed and possible experimental verification is described.
MSC:
| 92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |
| 26A33 | Fractional derivatives and integrals |
| 26E70 | Real analysis on time scales or measure chains |
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