The Marichev-Saigo-Maeda Fractional Calculus Operators Pertaining to the V-Function

Abstract

In the present paper, we establish some composition formulas for Marichev-Saigo-Maeda (MSM) fractional calculus operators with $V$-function as the kernel. In addition, on account of $V$-function, a variety of known results associated with special functions such as the Mittag-Leffler function, exponential function, Struve’s function, Lommel’s function, the Bessel function, Wright’s generalized Bessel function, and the generalized hypergeometric function have been discovered by defining suitable values for the parameters.