DYNAMICS OF COOPERATIVE REACTIONS BASED ON CHEMICAL KINETICS WITH REACTION SPEED: A COMPARATIVE ANALYSIS WITH SINGULAR AND NONSINGULAR KERNELS

Zubair Ahmad, Farhad Ali, Aisha M. Alqahtani, Naveed Khan and Ilyas Khan
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Zubair Ahmad: Department of Mathematics, City University of Science and Information Technology, Peshawar 25000, Khyber Pakhtunkhwa, Pakistan
Farhad Ali: Department of Mathematics, City University of Science and Information Technology, Peshawar 25000, Khyber Pakhtunkhwa, Pakistan
Aisha M. Alqahtani: ��Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia
Naveed Khan: Department of Mathematics, City University of Science and Information Technology, Peshawar 25000, Khyber Pakhtunkhwa, Pakistan
Ilyas Khan: ��Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-22

Abstract: Chemical processes are constantly occurring in all existing creatures, and most of them contain proteins that are enzymes and perform as catalysts. To understand the dynamics of such phenomena, mathematical modeling is a powerful tool of study. This study is carried out for the dynamics of cooperative phenomenon based on chemical kinetics. Observations indicate that fractional models are more practical to describe complex systems’ dynamics, such as recording the memory in partial and full domains of particular operations. Therefore, this model is modeled in terms of classical-order-coupled nonlinear ODEs. Then the classical model is generalized with two different fractional operators of Caputo and Atangana–Baleanu in a Caputo sense. Some fundamental theoretical analysis for both the fractional models is also made. Reaction speeds for the extreme cases of positive/negative and no cooperation are also calculated. The graphical solutions are achieved via numerical schemes, and the simulations for both the models are carried out through the computational software MATLAB. It is observed that both the fractional models of Caputo and Atangana–Baleanu give identical results for integer order, i.e. α = β = 1. By decreasing the fractional parameters, the concentration profile of the substrate S takes more time to vanish. Moreover, binding of first substrate increases the reaction rate at another binding site in the case of extreme positive cooperation, while the opposite effect is noticed for the case of negative cooperativity. Furthermore, the effects of other parameters on concentration profiles of different species are shown graphically and discussed physically.

Keywords: Cooperative Phenomena; Chemical Kinetics; Caputo; Atangana–Baleanu–Caputo (ABC) (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400485

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