A convective-diffusion equation with semi-infinite boundary conditions for rotating disk electrodes under the hydrodynamic conditions is discussed and analytically solved for electrochemical catalytic reactions. The steady-state catalytic current of the rotating disk electrode is derived for various possible values of parameters by using a new approach of the homotopy perturbation method. The theoretical approach in this paper is described, for the first time, on the basis of convection–diffusion equations for the kinetics of Fenton's reagent using a platinum rotating disk electrode. The obtained approximate analytical expression for the concentrations of ferric and ferrous ions for steady-state conditions are shown to be highly accurate when compared to numerical results and other approximations found in the literature. A sensitive analysis of parameters of the current and concentration is presented.