Anisotropic background for two fluids: matter and holographic dark energy

We discuss a spatially homogeneous and anisotropic Bianchi type-I space-time with two fluids as the content of the Universe: matter and holographic dark energy in the framework of general relativity. To get the exact solutions of Einstein's field equations, we choose the scale factor as a hyperbolic function, specifically, $a\left( t\right) =\sinh ^{\frac{1}{n}}\left( \gamma t\right) $, where $\gamma $ and $n>0$ are arbitrary constants, which gives us a time-dependent deceleration parameter. Then we study our cosmological model under the conditions of the parameters as: $\gamma $ fixed and $n>1$. Our cosmological solutions led to an early deceleration phase followed by the current observed acceleration phase. Further, the anisotropic parameter and some other physical parameters are discussed. We conclude that our cosmological model is consistent with the results of recent astronomical observations.