Novel Fractional Calculus Operators for Srivastava Polynomial and Special Functions

This paper explores the advanced framework of generalized fractional integral operators associated with Appell's function F3, as introduced by Saigo and Maeda.By extending the classical integral transformations, we establish four theorems governing the product of Srivastava polynomial, the generalized M-series and the multi-index Bessel functions.These results provide novel insights into the interaction of special functions within fractional calculus, enhancing the theoretical foundation and potential applications of these operators.Additionally, our study presents several new identities and generalizations, offering a deeper understanding of the interplay between fractional integration and differentiation with special functions.The findings contribute significantly to the ongoing development of fractional calculus and its applications in mathematical analysis and applied sciences.