Resumo

SAAD, Khaled M.  e  GOMEZ-AGUILAR, J.F.. Coupled reaction-diffusion waves in a chemical system via fractional derivatives in Liouville-Caputo sense. Rev. mex. fis. [online]. 2018, vol.64, n.5, pp.539-547.  Epub 30-Nov-2019. ISSN 0035-001X.

In this paper, we have generalized the fractional cubic isothermal auto-catalytic chemical system (FCIACS) with Liouville-Caputo, Caputo- Fabrizio-Caputo, and Atangana-Baleanu-Caputo fractional time derivatives, respectively. We apply the Homotopy Analysis Transform Method (HATM) to compute the approximate solutions of FCIACS using these fractional derivatives. We study the convergence analysis of HATM by computing the residual error function. Also, we find the optimal values of h so we assure the convergence of the approximate solutions. Finally we show the behavior of the approximate solutions graphically. The results obtained are very effectiveness and accuracy. 2010 Mathematics Subject Classification: 34A34, 35R11, 65M12, 26A33, 34A08, 35-XX.

Palavras-chave : Fractional isothermal auto-catalytic chemical systems; HATM; Liouville-Caputo fractional derivative; Caputo-Fabrizio fractional derivative; Atangana-Baleanu fractional derivative; h-curves; 02.30.Jr; 03.65.Fd; 04.20.Jb.

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