An analysis of the Yang 𝕐-function class extension through its incomplete functions

The new generalized hypergeometric function (Yang [Formula: see text]-function) described by the contour-type Mellin–Barnes integral representation serves as the inspiration for this study. The incomplete Yang [Formula: see text]-functions [Formula: see text] and [Formula: see text] that we shall introduce here are the appropriate extension of a class of [Formula: see text]-functions by merit of the gamma functions of incomplete type, [Formula: see text] and [Formula: see text]. In this work, our objective is to study several remarkable characteristics of these newly introduced incomplete [Formula: see text]-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 [Formula: see text]-functions. Further, we also propose the incomplete [Formula: see text]-functions [Formula: see text] and [Formula: see text] corresponding to a new generalization of the [Formula: see text]-function.