In this article, the kinetic mechanisms are based on Michaelis-Menten reaction in presence of substrate inhibition have been solved by techniques ‘Akbari-Ganji’s Method’ (AGM) and ‘Modified Adomian decomposition method’ (MADM). Comparisons of solution of dimensionless substrate and product concentrations for various kinetic mechanisms have been carried out using AGM, MADM and numerical simulation. We assessed the impact of Thiele modulus, dimensionless inhibition degree, and concentration of substances outside the support on changing nature of substrate and product concentrations within the boundary layer in this study. The obtained results depict that the used methods have good accuracy for different values of kinetic parameters. Furthermore, the mean integrated effectiveness factor has been derived for all the mechanisms employing AGM solutions. This paper clearly illustrates the distinctions between MADM and AGM.