Opial integral inequalities for generalized fractional operators with nonsingular kernel

We consider the well-known classes of functions U1(v,k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{U}_{1}(\mathbf{v},\mathtt{k})$\end{document} and U2(v,k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{U}_{2}(\mathbf{v},\mathtt{k})$\end{document}, and those of Opial inequalities defined on these classes. In view of these indices, we establish new aspects of the Opial integral inequality and related inequalities, in the context of fractional integrals and derivatives defined using nonsingular kernels, particularly the Caputo–Fabrizio (CF) and Atangana–Baleanu (AB) models of fractional calculus.