We have probed spatially homogeneous anisotropic Bianchi type-I universe in \(f(Q)\) gravity in the presence of dark matter, Tsallis holographic dark energy (THDE) and Rényi holographic dark energy (RHDE) were the goals of this research, where \(Q\) denotes the non-metricity scalar. It is presumable that the Lagrangian \(f(Q)\) depends linearly on \(Q\) . In order to arrive at the answer, the model parameter was constrained using the 30 observational Hubble data (OHD) in the range \(0 \le z \le 2.36\) . We estimated model parameter using the Markov Chain Monte Carlo (MCMC) approach and found that the model and observations appeared to be in good agreement. In order to find the precise solution of the field equations, we take into account a time-varying deceleration parameter (DP) in this work. This parameter creates an accelerating universe. For the foreseeable future of the universe’s evolution, the physical and kinematical characteristics of both hypotheses are thoroughly examined. Strong energy conditions (SEC) are in violation, indicating that the cosmos is expanding more quickly. But, weak energy conditions (WEC) and dominant energy conditions (DEC) are behaving positively, supporting the validity of the theory.
