Existence of fractional order semianalytical results for enzyme kinetics model

Hussam Alrabaiah,Amjad Ali,Fazal Haq,Kamal Shah

doi:10.1186/s13662-020-02897-2

Abstract

This research work investigates the existence of semianalytical solutions of a chemical kinematics model. We develop the conditions for the existence of the solutions for a proposed enzyme kinetics model, via tools of the fixed point theory. The semianalytical results were obtained with the help of Laplace transformation and Adomian decomposition method. The results established by the proposed techniques are in the form of infinite series. Furthermore, with extending homotopy perturbation method (HPM), we develop a series solutions for the considered model. By using Matlab, we present the approximate solution for both methods up to a few series terms.

Highlights

1 Introduction Recently, experimental evidence shows that dynamics problems in nature follow a fractional calculus analysis
Fractional calculus has a direct link to dynamical systems
Fractional differential equations (FDEs) present a novel technique developed to model phenomena related to the dynamics of the aforesaid fields of science [11,12,13,14]

Summary

Introduction

Experimental evidence shows that dynamics problems in nature follow a fractional calculus analysis. The researchers paid considerable attention to the aforementioned class of derivatives because they are more flexible and accurate compared with the classical derivatives, we refer the interested readers to [4, 28] Keeping these applications of fractional differential operator in mind, we introduce the following noninteger order enzyme kinematic system:. Lemma 1 In case of fractional differential equations, the following result holds: Iμ cDμh (τ ) = h(τ ) + ξ0 + ξ1τ + ξ2τ 2 + · · · + ξn–1τ n–1, where ξk is any real number, k is a positive integer up to n – 1 and the integral part of μ is denoted by [μ], while n = [μ] + 1.

Conclusions

Methods