Srivastava, H.M.AbuJarad, Eman S. A.Jarad, FahdSrivastava, GautamAbuJarad, Mohammad H. A.2022-11-132022-11-1320212021Srivastava, H. M., AbuJarad, E. S. A., Jarad, F., Srivastava, G., & AbuJarad, M. H. A. (2021). “The Marichev-Saigo-Maeda fractional-calculus operators involving the (p, q)-extended Bessel and Bessel-Wright functions.” Fractal and Fractional, 5(4), 210. https://doi.org/10.3390/fractalfract5040210https://doi.org/10.3390/fractalfract5040210http://hdl.handle.net/1828/14451The 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.enoperators of fractional calculus(p, q)-extensions of special functions(p, q)-extended Bessel function(p, q)-extended Gauss hypergeometric function(p, q)-extended Bessel-Wright functionFox-Wright functionMarichev-Saigo-Maeda fractional integral and fractional derivative operatorsEuler-Darboux partial differential equationArticleDepartment of Mathematics and Statistics