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

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Abstract.

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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Najran University, Najran, Saudi Arabia

    K. M. Saad

  2. Department of Mathematics, Faculty of Applied Science, Taiz University, Taiz, Yemen

    K. M. Saad

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  1. K. M. Saad
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Correspondence to K. M. Saad.

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Saad, K.M. Comparing the Caputo, Caputo-Fabrizio and Atangana-Baleanu derivative with fractional order: Fractional cubic isothermal auto-catalytic chemical system. Eur. Phys. J. Plus 133, 94 (2018). https://doi.org/10.1140/epjp/i2018-11947-6

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  • DOI: https://doi.org/10.1140/epjp/i2018-11947-6

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