In this paper, Fractional-time model for simply supported beams subjected to moving harmonic loads has been developed and studied numerically. Numerical fractional-time scheme coupled with the Galerkin method is elaborated to study the dynamical behavior of beams with fractional viscoelastic foundation, subjected to multiple harmonic moving loads and with a constant speed. Numerical results are obtained using the proposed methodological approach to study the effects of different system parameters, including, the load magnitude frequency, the order of the fractional derivative and the number of moving loads. The presented numerical technique is validated and compared with the Finite Element Method and the obtained results show a perfect agreement between the two methods.