ABSTRACT The anomalous diffusion and reaction process for Riemann-Liouville fractional differential equation is studied for heterogeneously isothermal nth-order reaction. The diffusion coefficient is regarded as a function of the position of the fractal porous catalyst. For a first-order irreversible reaction, new general analytical solutions of transient concentration profiles are derived with Mittag-Leffler function by taking into account of the intraparticle and external mass-transfer resistances. The numerical solution for anomalous diffusion-reaction is present for nth-order reaction; it is found that the results calculating by numerical solution are in satisfactory agreement with those by analytical solution for first-order reaction. The volume-averaged concentration and general expressions for effectiveness factor are present for first-order reaction. The effects of the order of the time fractional derivative, the fractal geometry of porous catalyst, diffusion coefficient, intraparticle and external mass-transfer resistances, and Thiele modulus on transient concentration profiles and catalytic efficiency are examined over a wide range of parameters by analytical solutions and numerical solution.