We introduce and analyze a mean-field model for polariton condensates which includes a velocity dependence of the effective polariton mass due to the photon and exciton components. The effective mass depends on the in-plane wave vector k, which at the inflection point of the lower polariton energy branch becomes infinite, and above this becomes negative. The polariton condensate modes of this mean-field theory are now sensitive to mass variations and, for certain points of the energy dispersion, the polariton condensate mode represents fractional quantum mechanics. The impact of the generalized kinetic-energy term is elucidated by numerical studies in two dimensions showing significant differences for large velocities. Analytical expressions for plane-wave solutions as well as a linear waves analysis show the significance of this model.