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].


Fractional Derivative Spherical Shell Special Important Case Lebesgue Measurable Function Ordinary Derivative 
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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Department Mathematical SciencesUniversity of MemphisMemphisUSA

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