Riemann—Liouville Fractional Multivariate Opial–type inequalities over a spherical shell

Here we introduce the concept of the Riemann—Liouville fractional radial derivative for a function defined on a spherical shell. Using polar coordinates we are able to derive multivariate Opial-type inequalities over a spherical shell of ℝ^N, N ≥ 2, by studying the topic in all possibilities. Our results involve one, two, or more functions. We also produce several generalized univariate fractional Opial-type inequalities, many of which are used to achieve the main goals. This treatment is based on [45].