In the present paper, we treat the problem of the existence of quark stars (QSs) for selected homogeneous and unpaired charge-neutral 3-flavor interacting quark matter with $\mathcal{O}(m_s^4)$ corrections equations of state (EoS). Using the EoS combined with the Tolmann-Oppenheimer-Volkoff (TOV) structure equations, the properties of stars are explored by obtaining their mass-radius relations. All calculations are carried out within the framework of the R-squared gravity defined by $f(R)=R+a{R}^2$. Our main goal is to discuss the effect for a wide range of the R-squared gravity parameter, a, on the mass-radius and the mass-central mass density $(M-{ϵ}_c)$ relation of QSs. Furthermore, we investigate the dynamical stability condition for those stars, and we show that their dynamical stability depends on the anisotropic parameters $B_{\perp }$ and $a_4^{\perp }$ coming from the respective EoS. In such a scenario our results provide circumstantial evidence in favor of super-massive pulsars.

在本文中，我们处理了选择的均质且不成对的电荷中性3味相互作用夸克物质的夸克星（QSs）存在的问题。 $\mathcal{Ø}（{米}_s^4）$校正状态方程（EoS）。通过结合EoS和Tolmann-Oppenheimer-Volkoff（TOV）结构方程，通过获得恒星的质量半径关系来探索恒星的特性。所有计算均在由以下公式定义的R平方引力的框架内进行$F（\mathrm{[R}）=\mathrm{[R}+\mathrm{一种}{\mathrm{[R}}^{\mathrm{2个}}$。我们的主要目标是讨论大范围的R平方重力参数a对质量半径和质量中心质量密度的影响$（\mathrm{中号}-{ϵ}_C）$QSs的关系。此外，我们研究了这些恒星的动力稳定性条件，并表明它们的动力稳定性取决于各向异性参数${乙}_{\perp }$ 和 ${\mathrm{一种}}_4^{\perp }$来自各自的EoS。在这种情况下，我们的结果提供了支持超级大质量脉冲星的间接证据。