The Marichev-Saigo-Maeda Fractional-Calculus Operators Involving the (p,q)-Extended Bessel and Bessel-Wright Functions
H. M. Srivastava, Eman S. A. AbuJarad, Fahd Jarad, Gautam Srivastava, Mohammed H. AbuJarad
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.