We analyze the cosmological solutions of f(T, B) gravity using dynamical system analysis where T is the torsion scalar and B be the boundary term scalar. In our work, we assume three specific cosmological models. For first model, we consider $$ f(T,B)=f_{0}(B^{k}+T^{m})$$f ( T , B ) = f 0 ( B k + T m ) , where k and m are constants. For second model, we consider $$f(T,B)=f_{0}T B$$f ( T , B ) = f 0 T B , for third model, we consider $$f(T,B)=\alpha T^{2}$$f ( T , B ) = α T 2 . We generate an autonomous system of differential equations for each models by introducing new dimensionless variables. To solve this system of equations, we use dynamical system analysis. We also investigate the critical points and their natures, stability conditions and their behaviors of Universe expansion. For first and second models, we get two stable critical points, while for third model we get one stable critical point. The phase plots of this system are analyzed in detail and study their geometrical interpretations also. For these three models, we evaluated density parameters such as $$\Omega _{r}$$Ω r , $$\Omega _{m}$$Ω m , $$\Omega _{\Lambda }$$Ω Λ and $$\omega _{eff}$$ω eff and deceleration parameter (q) and find their suitable range of the parameter $$\lambda $$λ for stability. For first model, we get $$\omega _{eff}=-0.833,-0.166$$ω eff = - 0.833 , - 0.166 and for second model, we get $$\omega _{eff}=-\frac{1}{3}$$ω eff = - 1 3 . This shows that both the models are in quintessence phase. For third model we get accelerated expansion of the Universe. Further, we compare the values of EoS parameter and deceleration parameter with the observational values.

In this paper, using the recently introduced f(T) gravity framework, we have analyzed the viscous fluid cosmological model in FLRW cosmological model by assuming a specific form of the bulk viscosity coefficient as, ζ = ζ 0 + ζ 1 H + ζ 2 H ̇ H + H and a non-linear f(T) model particularly, f ( T ) = T − α − T where α is the model parameter. The bulk viscosity coefficients are estimated by using Hubble 31 data set. Using the phase space technique, we examine the asymptotic behaviour of our cosmological bulk viscous model. We found one stable critical point. Phase space analysis and the geometrical interpretations are given. We discover that according to our model, the Universe evolved from a matter-dominated decelerated phase (a past attractor) to a stable de-Sitter accelerated epoch (a future attractor). The evolution of EoS parameter shows the acceleration phase of the cosmic expansion whereas the negative behavior of viscosity-induced pressure indicates the accelerated expansion of the Universe. Additionally, the cosmic matter-energy density exhibits positive behavior. We look into how statefinder parameters behave for our model . We discover that the trajectory of our model starts at the quintessence and ends at the ΛCDM region. We use the Om diagnostic test, which reveals that our model displays quintessence behaviour. The energy condition criteria are analyzed, and we discover that SEC has been violated, whereas WEC, NEC and DEC satisfy the positivity criteria. Our f(T) cosmological model, with the influence of bulk viscosity successfully describes the expansion history of the Universe and provides a good fit to recent observational data.