A theory of diffusion-influenced geminate and pseudo-first-order bulk reactions on fractal structures is presented within the Smoluchowski framework. The formalism is based on the solution of the backward equation for the pair survival probability, generalized to noninteger dimensionality using the effective potential approximation. Possible anomalous diffusion is taken into account by assuming a new time variable, ensuring linear asymptotics of the mean-squared displacement. The results for both absorbing and radiation inner boundary conditions are derived for noninteracting reactants and compared with those well known for integer dimensions. The asymptotic analysis for arbitrary potential is also carried out.