Comparing the Caputo, Caputo-Fabrizio and Atangana-Baleanu derivative with fractional order: Fractional cubic isothermal auto-catalytic chemical system

In this work we extend the standard model for a cubic isothermal auto-catalytic chemical system (CIACS) to a new model of a fractional cubic isothermal auto-catalytic chemical system (FCIACS) based on Caputo (C), Caputo-Fabrizio (CF) and Atangana-Baleanu in the Liouville-Caputo sense (ABC) fractional time derivatives, respectively. We present approximate solutions for these extended models using the q-homotopy analysis transform method (q-HATM). We solve the FCIACS with the C derivative and compare our results with those obtained using the CF and ABC derivatives. The ranges of convergence of the solutions are found and the optimal values of h, the auxiliary parameter, are derived. Finally, these solutions are compared with numerical solutions of the various models obtained using finite differences and excellent agreement is found.