Abstract
Our main aim in this article is to introduce and investigate a new model of fractional-order quadratic autocatalysis with linear inhibition. In particular, we evaluate the approximate solutions of this model by means of the power law, the exponential law and the Mittag-Leffler kernel. The approximate solutions are based upon the fundamental theorem of fractional calculus as well as the Lagrange polynomial interpolation. We compare the approximate solutions with that derived by using the finite-difference method, thereby showing excellent agreement which we have found by applying the power law and the Mittag-Leffler kernel. We study the effect of the variation the fractional-order on the behavior of the solutions due to the presence of definitions of new fractional-calculus operators. We observe the chaotic fractional behavior and illustrate the chaotic fractional-order quadratic autocatalysis with linear inhibition system by plotting the solutions in the plane. (C) 2019 Elsevier Ltd. All rights reserved.