In this work, a generalized reaction-diffusion model useful to study the interactions between anomalous diffusion and chemical reactions in catalyst particles is presented. The fractional reaction-diffusion model considers the linearization of the non-linear reaction kinetic terms, which allows the solution of the mathematical model through the Fourier transform. The proposed methodology can be used for the dynamic analysis of the concentration profiles in the catalytic pellets, including internal and external mass transfer resistances, as well as for the estimation of effectiveness factor (EF). These findings revealed that the analysis of dynamic reaction-diffusion linearized models where the mass transfer is described by the anomalous transport can be analysed in the frequency domain. Two kinetic models, a general power-law and Langmuir-Hinshelwood, were considered. The results demonstrated the effect of use the traditional Fick's law and the anomalous transport (i.e., subdiffusion or superdiffusion phenomena) in a porous media system, particularly on the space-time concentration profile predictions and the influence on the effectiveness factor of the catalytic particle.