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Iyengar-Hilfer fractional inequalities

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  • Here we present Iyengar type integral inequalities. At the univariate level they involve $ \psi $-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 $ \left \Vert \cdot \right \Vert _{p} $, $ 1\leq p\leq \infty $. At the end we provide an application.

    Mathematics Subject Classification: 26A33, 26D10, 26D15.


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    [8] Ž. TomovskiR. Hilfer and H. M. Srivastava, Fractional and operational calculus with generalized fractional derivative operators and Mittag-Leffler type functions, Integral Transforms Spec Funct., 21 (2010), 797-814.  doi: 10.1080/10652461003675737.
    [9] J. Vanterler da C. Sousa and E. Capelas de Oliveira, On the $\psi $-Hilfer fractional derivative, Commun. Nonlinear Sci. Numer. Simul., 60 (2018), 72-91.  doi: 10.1016/j.cnsns.2018.01.005.
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