Comparing the Caputo, Caputo-Fabrizio and Atangana-Baleanu derivative with fractional order: Fractional cubic isothermal auto-catalytic chemical system
Department of Mathematics, Faculty of Arts and Sciences, Najran University, Najran, Saudi Arabia
2 Department of Mathematics, Faculty of Applied Science, Taiz University, Taiz, Yemen
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Accepted: 24 January 2018
Published online: 7 March 2018
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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018