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An analysis of the Yang 𝕐-function class extension through its incomplete functions
International Journal of Geometric Methods in Modern Physics ( IF 2.1 ) Pub Date : 2024-05-07 , DOI: 10.1142/s0219887824400218
K. Kritika 1 , S. D. Purohit 2, 3
Affiliation  

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 γ𝕐r,sp,q(z) and Γ𝕐r,sp,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, γ(σ,x) and Γ(σ,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 γ𝕎p,qr,s and Γ𝕎p,qr,s corresponding to a new generalization of the 𝕐-function.



中文翻译:

通过不完全函数分析Yang𝕐函数类扩展

新的广义超几何函数(Yang𝕐-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γ𝕐r,sp,qzγ𝕐r,sp,qz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,γσ,Xγσ,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γ𝕎p,qr,sγ𝕎p,qr,s对应于新的概括𝕐-功能。

更新日期:2024-05-07
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