**Authors:** Z. Vosika, G. Lazović

In this paper we develop the new physicalmathematical time scale kinetic approach-model applied on organic and non-organic particles motion. Concretely, here, at first, this new research approach is based on enzyme particles dynamics results. At the beginning, a time scale is defined to be an arbitrary closed subset of the real numbers R, with the standard inherited topology. Mathematical examples of time scales include real numbers R, natural numbers N, integers Z, the Cantor set (i.e. fractals), and any finite union of closed intervals of R. Calculus on time scales (TSC) was established in 1988 by Stefan Hilger. TSC, by construction, is used to describe the complex process. This method may utilized for description of physical (classical mechanics), material (crystal growth kinetics, physical chemistry kinetics - for example, kinetics of barium-titanate synthesis), (bio)chemical or similar systems and represents major challenge for contemporary scientists. In this sense, the MichaelisMenten (MM) mechanism is the one of the best known and simplest nonlinear biochemical network which deserves appropriate attention. Generally speaking, such processes may be described of discrete time scale. Reasonably it could be assumed that such a scenario is possible for MM mechanism. In this work, discrete time MM kinetics (dtMM) with time various step h, is investigated. Instead of the first derivative by time used first backward difference h. Physical basics for new time scale approach is a new statistical thermodynamics, natural generalization of Tsallis non-extensive or similar thermodynamics. A reliable new algorithm of novel difference transformation method, namely multi-step difference transformation method (MSDETM) for solving system of nonlinear ordinary difference equations is proposed. If h tends to zero, MSDETM transformed into multi-step differential transformation method (MSDTM). In the spirit of TSC, MSDETM describes analogously MSDTM.

**Comments:** 7 Pages.

**Download:** **PDF**

[v1] 2016-07-09 08:03:25

**Unique-IP document downloads:** 23 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful. *