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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.

abstract and applied analysis

The Marichev-Saigo-Maeda Fractional Calculus Operators Pertaining to the <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mi>V</mi> </math>-Function

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

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