Abstract

SAAD, Khaled M.. A different approach for the fractional chemical model. Rev. mex. fis. [online]. 2022, vol.68, n.1.  Epub June 23, 2023. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.68.011404.

This article analyzes and compares the two algorithms for the numerical solution of fractional isothermal chemical equations (FICEs) based on mass action kinetics for autocatalytic feedback. The chemical reaction involves the conversion of a reactant in the Liouville-Caputo sense. The first method is based on the spectral collocation method (SCM), for which properties of Legendre polynomials are utilized to reduce the FICEs to a set of algebraic equations. We then use the Newton-Raphson method (NRM) to solve the resulting set of algebraic equations. The second method is based on properties of Newton polynomial interpolation (NPI) and the fundamental theorem of fractional calculus. We utilize both methods to construct numerical solutions of FICEs. The accuracy and effectiveness of both methods are verified by calculating the absolute error with numerical solutions and good agreement is found in all cases.

Keywords : Liouville-Caputo operator; fractional isothermal chemical; Legendre polynomials; spectral collocation method; Newton polynomial interpolation; Newton-Raphson method.

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