Iyengar-Hilfer fractional inequalities

Abstract

<p style='text-indent:20px;'>Here we present Iyengar type integral inequalities. At the univariate level they involve <inline-formula><tex-math id="M1">\begin{document}$ \psi $\end{document}</tex-math></inline-formula>-Hilfer left and right fractional derivatives. At the multivariate level they involve Hilfer left and right fractional derivatives, and they deal with radial and non-radial functions on the ball and spherical shell. All estimates are with respect to norms <inline-formula><tex-math id="M2">\begin{document}$ \left \Vert \cdot \right \Vert _{p} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M3">\begin{document}$ 1\leq p\leq \infty $\end{document}</tex-math></inline-formula>. At the end we provide an application.</p>