Siberian Federal University

This paper investigates incomplete R-function expansion formulae from a fractional calculus perspective. We reveal the underlying links between fractional calculus operators and incomplete R- functions through rigorous mathematical computation and analysis. Through the taking advantage of the Leibniz formula within fractional differentiation, our goal is towards acquire new expansion formulae that provide new perspectives on the characteristics and behavior of these functions. The findings of this investigation creates new directions regarding the study of fractional calculus image formulas with incomplete R-functions and new ways to advance scientific understanding. As a particular illustration to demonstrate our main findings, expansion formulas for additional special functions as well as incomplete functions are derived