Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682212Special Issue20211210Interacting anisotropic dark energy with time dependent inhomogeneous equation of state21672180607610.22075/ijnaa.2021.6076ENMd Khurshid AlamDepartment of Mathematics, NIT Manipur, Imphal-795004, IndiaS. Surendra SinghDepartment of Mathematics, NIT Manipur, Imphal-795004, IndiaJournal Article20211008The interaction of dark energy in the LRS Bianchi type-$I$ line element is explored on the background of $f(R,T)$ gravity, where $R$ and $T$ denotes the Ricci scalar together with the trace of energy momentum tensor of matter respectively. Here modified field equations are calculated using $f(R,T)=f_1 (R)+f_2 (T)$ together with inhomogeneous equation of state $(EoS)$, $p=\omega \rho -\Lambda (t)$, where $\omega$ is constant. The solutions of modified Einstein field equations (EFE) obtained are solved by taking a periodic time varying deceleration parameter (DP). Our model shows periodic nature with Big-Bang prevailing at time $t=0$. An investigation is done on the energy conditions and found that the conditions of null energy and strong energy are found to be violated. We analyse the geometrical and physical behaviours of these models.https://ijnaa.semnan.ac.ir/article_6076_e438e18aa8c99ee74c6cf4d8f35b1f7a.pdf