In this work, the solutions of traversable wormholes are investigated inside modified [Formula: see text] gravity under non-commutative geometry since matter possesses Lorentzian density distribution of a particle-like gravitation source. To find the exact wormhole solutions, two different shape functions [Formula: see text], [Formula: see text], and [Formula: see text], [Formula: see text], are considered. The first shape function was proposed by Mishra and Sharma [A new shape function for wormholes in [Formula: see text] gravity and General Relativity, preprint (2020), arXiv:2003.00298v1 [physics.gen-ph]], however the second is newly defined in this paper. The behaviors of both shape functions are analyzed with the throat radius [Formula: see text]. The equation-of-state (EoS) parameter energy conditions, and anisotropy parameter are discussed with graphical point of view.

中文翻译：

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具有非交换几何和洛伦兹分布的 f(R) 理论中虫洞的两种不同形状函数

在这项工作中，由于物质具有类粒子引力源的洛伦兹密度分布，因此研究了非交换几何下修改后的[公式：见文本]引力内的可穿越虫洞的解。为了找到确切的虫洞解，考虑了两个不同的形状函数[公式：见文本]、[公式：见文本]和[公式：见文本]、[公式：见文本]。第一个形状函数是由 Mishra 和 Sharma [A new shape function for wormholes in [Formula: see text]gravity and General Relativity, preprint (2020), arXiv:2003.00298v1 [physics.gen-ph]] 提出的，但是第二个是本文新定义的。两种形状函数的行为都用喉部半径进行分析[公式：见正文]。状态方程 (EoS) 参数能量条件，