Recent empirical and numerical evidence shows that the Basset force plays an important role in the description of acceleration of relatively small sediment particles moving close to solid boundaries. This force can make the numerical solution of the equations of motion computationally time and memory consuming. This technical note presents a two-stage methodology to deal with the difficulties associated with computing the Basset force. The Basset term is first approximated based on a semiderivative (fractional mathematics), and then the integration time is redefined in terms of appropriate flow and particle time scales, thus, avoiding unnecessary computations. Important savings in computational time are reported.