Interaction of Anisotropic Dark Energy with Generalized Hybrid Expansion Law

Interaction of dark energy in the anisotropic locally rotationally symmetric (LRS) Bianchi type-I metric is investigated in the context of modified $f\left(R,T\right)$ theory of gravity, where $R$ is the Ricci scalar and $T$ is the trace of stress energy momentum tensor. We choose the particular form of the functional $f\left(R,T\right)=f_1\left(R\right)+f_2\left(T\right)$ ; then, we find the exact solutions of the field equations by applying inhomogeneous equation of state, $p=\omega \rho -\Lambda \left(t\right)$ , and a generalized form of hybrid expansion law. The transition of deceleration to acceleration is observed in this model. It is also observed that the universe shows accelerated expansion at late epoch. The derived model overlaps with $\Lambda \text{CDM}$ at late time which is in agreement with present observation. Energy conditions of the derived model are also investigated. From the plot, we observe the age of universe $\left(t_0\approx 13.821\text{Gyr}\right)$ for the observed $H_0\approx 70.07{\text{Kms}}^{‐1}{\text{Mpc}}^{‐1}$ . The physical and geometrical behaviours of these models are also discussed.