Here we have studied locally rotationally symmetric Bianchi-V Universe in the presence of modified theory for gravitation [$ f (R, T )$ theory] and for that, we considered a perfect fluid with heat conduction as the energy source. We used the law of variation for the deceleration parameter (DP) to solve field equations, as it gives a constant value of DP and is related to the average scale factor metric. Also, we have discussed the physical and geometrical properties of the model in detail.

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.