Operators of Fractional Calculus and Associated Integral Transforms of the (r,s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\mathfrak {r}}, {\mathfrak {s}})$$\end{document}-Extended Bessel–Struve Kernel Function

Present paper contains Marichev–Saigo–Maeda fractional integration and differentiation formulas and certain Integral transforms of the involving (r,s)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\mathfrak {r}}, {\mathfrak {s}})$$\end{document}-extended Bessel–Struve kernel function. Several particular cases of the leading findings are derived for the Saigo’s, Riemann–Liouville and Erdélyi–Kober fractional (arbitrary order) integration and fractional differentiation formulas.