The Marichev-Saigo-Maeda fractional-calculus operators involving the (p, q)-extended Bessel and Bessel-Wright functions

Abstract

The goal of this article is to establish several new formulas and new results related to the Marichev-Saigo-Maeda fractional integral and fractional derivative operators which are applied on the (p, q)-extended Bessel function. The results are expressed as the Hadamard product of the (p, q)- extended Gauss hypergeometric function Fp,q and the Fox-Wright function rΨs(z). Some special cases of our main results are considered. Furthermore, the (p, q)-extended Bessel-Wright function is introduced. Finally, a variety of formulas for the Marichev-Saigo-Maeda fractional integral and derivative operators involving the (p, q)-extended Bessel-Wright function is established.