Fractal-fractional Brusselator chemical reaction

Abstract

In this paper, we replace the classical differential operators with the fractal-fractional differential operators corresponding to the power law, exponential decay, and the generalized Mittag-Leffler kernels. These operators have two parameters created: the first is a fractal dimension and the second is a fractional order. The numerical schemes are combination of the Lagrange interpolating polynomial and theory of fractional calculus. In the case of δ=k=1 the numerical solutions for the proposed models are found to be in an excellent agreement with the finite difference methods. We investigate the effects of the fractal-fractional order on the oscillations in the Fractal-Fractional Brusselator Chemical Reaction (FFBCR). All calculations in this paper were done using the mathematica package.