The objective of the present research article is to study the δ-Lorentzian trans-Sasakian manifolds conceding the η-Ricci solitons and gradient Ricci soliton. We shown that a symmetric second order covariant tensor in a δ-Lorentzian trans-Sasakian manifold is a constant multiple of metric tensor. Also, we furnish an example of η-Ricci soliton on 3-diemsional δ-Lorentzian trans-Sasakian manifold is provide in the region where δ-Lorentzian trans-Sasakian manifold is expanding. Furthermore, we discuss some results based on gradient Ricci solitons on $3$-dimensional δ- Lorentzian trans-Sasakian manifold.
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Siddiqi et al. (2021) studied this question.