The present paper deals with flat Friedmann–Robertson–Walker (FRW) model with two-fluid sources in fractal cosmology. One fluid in this model represents the Universe’s matter content, while the other is a radiation field that models the cosmic microwave background. To obtain the deterministic model, we used the pressure– density relationship for matter via the gamma law equation of state pm = (γ − 1) ρm, 1 ≤ γ ≤ 2. The solutions of fractal field equations are obtained in terms of Kummer’s confluent hypergeometric function of the first kind.Some physical parameters of the models are obtained and their behaviour is discussed in detail using graphs.