This paper encompassed various physically realistic models of static and spherically symmetric wormholes in extended $f(R)$ gravitational framework by incorporating the features of non-compact matter density distribution of non-commutative geometry. For this assessment, we formulated the $f(R)$ field equations and obtained their exact analytical solutions in presence of cosmologically well-consistent power law type $f(R)=a{R}^n$ corresponding to distinct values of the parameter $n$. We conducted the physical adequacy of such proposed solutions through the graphical manifestation for the necessary existence of wormhole structures. Moreover, we revisited our field equations with a feasible choice of shape function together with reconstructed form of $F(R)$ to provide an again authentication to the existence of wormholes structures. These all implications vigorously depicted that our discussed models are able to expect the required wormhole structures.

本文涵盖了扩展中静态和球对称虫洞的各种物理现实模型$F(R)$通过结合非交换几何的非紧凑物质密度分布的特征来构建引力框架。对于此评估，我们制定了$F(R)$场方程并在存在宇宙学良好一致的幂律类型的情况下获得它们的精确解析解$F(R)=\mathrm{一个}{R}^n$对应于参数的不同值$n$. 我们通过虫洞结构必要存在的图形化表现形式，对此类提出的解决方案的物理充分性进行了验证。此外，我们通过形状函数的可行选择以及重构形式重新审视了我们的场方程$F(R)$为虫洞结构的存在提供再次验证。这些所有含义都有力地描述了我们讨论的模型能够预期所需的虫洞结构。