In this paper, a fractional-order model is developed for representing the fuel propagation in a specific part of electro-injectors of common rail injection systems. The considered element is a pipe connecting the common rail to the accumulation volume from which the fuel is sent to the nozzles. The model extends the Navier-Stokes partial differential equations that can not be analytically solved in such case. The generalized continuity and momentum equations include different fractional orders of differentiation. Moreover, a novel numerical technique is proposed to find an approximate solution. The approach is tested by comparison with real data.