Coupled reaction-diffusion waves in a chemical system via fractional derivatives in Liouville-Caputo sense

Authors

  • Francisco Gomez CONACyT-Tecnológico Nacional de México/CENIDET. Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México. http://orcid.org/0000-0001-9403-3767
  • Khaled Saad Department of Mathematics. Faculty of Arts and Sciences. Najran University, Saudi Arabia.

DOI:

https://doi.org/10.31349/RevMexFis.64.539

Keywords:

Fractional isothermal auto-catalytic chemical systems, HATM, Liouville-Caputo fractional derivative, Caputo-Fabrizio fractional derivative, Atangana-Baleanu fractional derivative, h-curves.

Abstract

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.

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Published

2018-08-31

How to Cite

[1]
F. Gomez and K. Saad, “Coupled reaction-diffusion waves in a chemical system via fractional derivatives in Liouville-Caputo sense”, Rev. Mex. Fís., vol. 64, no. 5 Sept-Oct, pp. 539–547, Aug. 2018.

Issue

Vol. 64 No. 5 Sept-Oct (2018): Revista Mexicana de Física

Section

14 Other areas in Physics

License

Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.