Composition Formula for Saigo Fractional Integral Operator Associated with V‐Function

Abstract

In this study, we form integral formulas for Saigo’s hypergeometric integral operator involving V‐function. Corresponding assertions for the classical Riemann–Liouville (R‐L) and Erdélyi–Kober (E‐K) fractional integral operator are extrapolated. Also, by putting in the transformations of Beta and Laplace, we can establish their composition formulas. By selecting the appropriate parameter values, the V‐function may be reduced to a variety of functions, including the exponential function, Mittag–Leffler, Lommel, Struve, Wright’s generalized Bessel function, and Bessel and generalized hypergeometric function.