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We investigate a new class of LRS Bianchi type-II cosmological models byrevisiting in the paper of Mishra {\it et al} (2013) by considering a newdeceleration parameter (DP) depending on the time in string cosmology for themodified gravity theory suggested by S$\acute{a}$ez \& Ballester (1986). Wehave considered the energy-momentum tensor proposed by Leteliar (1983) for bulkviscous and perfect fluid under some assumptions. To make our models consistentwith recent astronomical observations, we have used scale factor (Sharma {\itet al} 2018; Garg {\it et al} 2019) $ a(t)=\exp{[\frac{1}{\beta}\sqrt{2 \beta t+ k}]}$, where $\beta $ and $k$ are positive constants and it provides atime-varying DP. By using the recent constraints ($H_{0}=73.8$, and $q_{0} =-0.54$) from SN Ia data in combination with BAO and CMB observations (Giostri{\it et al}, arXiv:1203.3213v2[astro-ph.CO]), we affirm $\beta = 0.0062$ and $k= 0.000016$. For these constraints, we have substantiated a new class ofcosmological transit models for which the expansion takes place from earlydecelerated phase to the current accelerated phase. Also, we have studied somephysical, kinematic and geometric behavior of the models, and have found themconsistent with observations and well established theoretical results . We havealso compared our present results with those of Mishra {\it et al} (2013) andobserved that the results in this paper are much better, stable underperturbation and in good agreement with cosmological reflections.

Anisotropic bulk viscous string cosmological models of the Universe under a time-dependent deceleration parameter