Abstract
Our main aim in this paper is to propose and investigate new models of fractional blood ethanol and fractional two-cell cubic autocatalysis reaction models. In particular, we evaluate the numerical solutions of these models by means of the power law and the Mittag-Leffler kernel. The numerical solutions are based mma7188 the fundamental theorem of fractional calculus as well as the Lagrange polynomial interpolation. We compare the numerical solutions for the blood ethanol with exact solutions while for the two-cell cubic autocatalysis reaction model, we compare with numerical solutions that derived by using the finite-difference method. In the case of the fractional order of the second model, the comparison is made with the spectral collocation method. In all cases, we found an excellent agreement. The novelty of this work is to study these models with the proposed algorithm for first time. Finally, we illustrate the behaviors of the numerical solutions for different values of order of the models and their parameters.