Iyengar-Hilfer fractional inequalities

George A. Anastassiou

doi:10.3934/mfc.2021004

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2021, Volume 4, Issue 4: 221-252. Doi: 10.3934/mfc.2021004

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Iyengar-Hilfer fractional inequalities

George A. Anastassiou

Department of Mathematical Sciences, University of Memphis, Memphis, TN 38152, USA

Received: January 31, 2021

Early access: March 2021

Published: November 2021

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Abstract

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.

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

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References

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