Dynamics of two-step reversible enzymatic reaction under fractional derivative with Mittag-Leffler Kernel

Abstract

Chemical kinetics is a branch of chemistry that is founded on understanding chemical reaction rates. Chemical kinetics relates many aspects of cosmology, geology, and even in some cases of, psychology. There is a need for mathematical modelling of these chemical reactions. Therefore, the present research is based on chemical kinetics-based modelling and dynamics of enzyme processes. This research looks at the two-step substrate-enzyme reversible response. In the two step-reversible reactions, substrate combines with enzymes which is further converted into products with two steps. The model is displayed through the flow chart, which is then transformed into ODEs. The Atangana-Baleanu time-fractional operator and the Mittag-Leffler kernel are used to convert the original set of highly nonlinear coupled integer order ordinary differential equations into a fractional-order model. Additionally, it is shown that the solution to the investigated fractional model is unique, limited, and may be represented by its response velocity. A numerical scheme, also known as the Atangana-Toufik method, based on Newton polynomial interpolation technique via MATLAB software, is adopted to find the graphical results. The dynamics of reaction against different reaction rates are presented through various figures. It is observed that the forward reaction rates increase the reaction speed while backward reaction rates reduce it.

On a class of piece-wise fractional order derivative delay differential equation with integral type condition

“…These ideas have recently been used as the foundation for breaking down numerous mathematical problems. See, for instance [2,15,36] and the references contained therein. For more sophisticated applications of dynamical systems studied using fractional calculus, we refer to [4,14,24,33].…”

On boundary values system of sequential hybrid fractional differential equations

“…In additions, the said area have been used increasingly to investigate various viral infectious diseases including Hepatitis B, and others in [12,13,28,29]. Moreover some interesting applicable in fluid mechanics, vegetable oil process, electromagnetic theory, pine wilt disease can be read in the cited articles as [1,16,[22][23][24].…”

Forecasting and dynamical modeling of reversible enzymatic reactions with a hybrid proportional fractional derivative

“…This type of kinetics research can shed light on the catalytic mechanism of an enzyme and its role in metabolism. Furthermore, understanding how a drug or modifier might affect behavior and how it might affect the reaction rate is essential [3]. Leonor Michaelis and Maud Leonora Menten discovered the equation expressing enzymatic rates over a century ago.…”

“…It is rare to study the kinetics of two-step reversible biological processes with fractional-order mathematical models. The model proposed in [3] is resolved in this work using generalized proportional derivatives. This remainder of this article is organized as follows:…”