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Modeling Riemann-Liouville fractional differential equations for diffusion and reaction in fractal porous media. (English) Zbl 1466.92307

Summary: In this article, Riemann-Liouville fractional differential equations for diffusion and reaction process in batch reactors are developed with Mittag-Leffler function. For first-order irreversible reaction under isothermal conditions, analytical solutions are derived for fractal porous catalyst by taking into account intraparticle diffusion and external mass-transfer resistances. Furthermore, a numerical method for Riemann-Liouville fractional differential equations is developed. Both analytical and numerical solutions are found in good agreement with each other. The general expressions for effectiveness factor for first-order reaction under isothermal conditions are derived for fractal porous catalyst. Lastly, the effects of different parameters are studied.

MSC:

92E20 Classical flows, reactions, etc. in chemistry
35K57 Reaction-diffusion equations

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