Images for the Y-Function via Marichev–Saigo–Maeda Fractional Integration and Differentiation Operators

The Y-function has emerged as a significant tool in generalized fractional calculus due to its ability to unify and extend numerous classical special functions and hypergeometric-type functions. Applying the Marichev–Saigo–Maeda fractional integration and differentiation operators of any complex order to the Y-function, this study establishes four theorems. These generalized fractional operators yield transformed expressions that increase the order of the Y-function while preserving its structural form, thereby demonstrating the function’s intrinsic compatibility with fractional operators. Explicit formulations are further derived for the Saigo, Erdélyi–Kober, Riemann–Liouville, and Weyl fractional integrals and derivatives. The results strengthen the theoretical foundation of the Y-function and provide deeper insight into its role within the framework of fractional calculus.