Analysis of reaction-diffusion system via a new fractional derivative with non-singular kernel

In this paper, we obtain analytical solutions for the fractional cubic isothermal auto-catalytic chemical system with Caputo-Fabrizio and Atangana-Baleanu fractional time derivatives in Liouville-Caputo sense. We utilize the q-homotopy analysis transform method to compute the approximate solutions. We find the optimal values of h so we assure the convergence of the approximate solutions. Finally, we compare our results numerically with the finite difference method and excellent agreement is found.