Mathematical study of a memory induced biochemical system

In this work, to study the effect of memory on a bi-substrate enzyme kinetic reaction, we have introduced an approach to fractionalize the system, considering it as a threecompartmental model. Solutions of the fractionalized system are compared with the corresponding integer-order model. The equilibrium points of the fractionalized system are derived analytically. Their stability properties are discussed from numerical aspect. We determine the changes of the substances due to the changes of “ memory effect ”. The effect is discussed critically from the perspective of product formation. We have also analyzed the memory induced system with a control measure in view of optimizing the product. Our numerical result reveals that the solutions of the fractionalized system, when it is free from memory, are in good agreement with the integer-order system. It is noticed that the effect of memory influences the reaction in the forward direction and assists in yielding the product more quickly. However, an extensive use of memory makes the system slower, but introduction of a control input makes the reaction faster. It is possible to overcome the slowness of the reaction due to the undue effect of memory by appropriate use of a control measure.