The new generalized hypergeometric function (Yang $𝕐$-function) described by the contour-type Mellin–Barnes integral representation serves as the inspiration for this study. The incomplete Yang $𝕐$-functions ${}^{\gamma }{𝕐}_{r,s}^{p,q}(z)$ and ${}^{\mathrm{\Gamma }}{𝕐}_{r,s}^{p,q}(z)$ that we shall introduce here are the appropriate extension of a class of $𝕐$-functions by merit of the gamma functions of incomplete type, $\gamma (\sigma ,x)$ and $\mathrm{\Gamma }(\sigma ,x)$. In this work, our objective is to study several remarkable characteristics of these newly introduced incomplete $𝕐$-functions viz; reduction formula, derivative, various integral transformations. Additionally, using these newly established incomplete functions, we formulate and solve a generalized fractional kinetic equation in terms of these incomplete $𝕐$-functions. Further, we also propose the incomplete $𝕎$-functions ${}^{\gamma }{𝕎}_{p,q}^{r,s}$ and ${}^{\mathrm{\Gamma }}{𝕎}_{p,q}^{r,s}$ corresponding to a new generalization of the $𝕐$-function.

新的广义超几何函数（Yang$𝕐$-函数）由轮廓型 Mellin-Barnes 积分表示描述，是本研究的灵感来源。不完整的阳$𝕐$-功能${}^{\gamma }{𝕐}_{r,s}^{p,q}（z）$和${}^{\mathrm{\gamma }}{𝕐}_{r,s}^{p,q}（z）$我们在这里要介绍的是一类的适当扩展$𝕐$- 不完全类型伽玛函数的优点的函数，$\gamma （\sigma ,X）$和$\mathrm{\gamma }（\sigma ,X）$。在这项工作中，我们的目标是研究这些新引入的不完整的一些显着特征$𝕐$- 功能即；约简公式、导数、各种积分变换。此外，使用这些新建立的不完全函数，我们根据这些不完全函数制定并求解广义分数阶动力学方程$𝕐$-功能。此外，我们还提出了不完整的$𝕎$-功能${}^{\gamma }{𝕎}_{p,q}^{r,s}$和${}^{\mathrm{\gamma }}{𝕎}_{p,q}^{r,s}$对应于新的概括$𝕐$-功能。