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The objective of the present research article is to study  the $\delta$-Lorentzian trans-Sasakian manifolds conceding  the $\eta$-Ricci solitons and gradient Ricci soliton. We shown that a symmetric second order covariant tensor in a $\delta$-Lorentzian trans-Sasakian manifold is a constant multiple of metric tensor. Also, we furnish  an example of $\eta$-Ricci soliton on 3-diemsional $\delta$-Lorentzian trans-Sasakian manifold is provide in the region where $\delta$-Lorentzian trans-Sasakian manifold is expanding. Furthermore, we  discuss some results based on gradient Ricci solitons on $3$-dimensional $\delta$- Lorentzian trans-Sasakian manifold.

$\eta$-RICCI SOLITONS AND GRADIENT RICCI SOLITONS ON $\delta$- LORENTZIAN TRANS-SASAKIAN MANIFOLDS