Iyengar-Hilfer fractional inequalities
type: Item
instance of: scholarly article
title: Iyengar-Hilfer fractional inequalities
zbMATH Open document ID: 1490.26014
author: George A. Anastassiou
published in: Mathematical Foundations of Computing
publication date: 2022-01-11T00:00:00Z
review text: \textit{K. S. K. Iyengar} [Math. Stud. 6, 75--76 (1938; JFM 64.0209.02)] obtained the following classical inequality: if \(f\) is a differentiable function on the real interval \([a,b]\) and \(| f'(x)| \leq M,\) then \[\Bigl| \int^{b}_{a}f(x)dx-\frac{1}{2}(b-a)(f(a)+f(b))\Bigr| \leq \frac{M(b-a)^2}{4} -\frac{(f(b)-f(a))^2}{4M}.\] The above result is often referred to as Iyengar inequality in the literature. In this paper, the author presents Iyengar-type inequalities involving the \(\Psi\)-Hilfer and Hilfer left and right fractional derivatives with respect to norms \(\| . \|_p\), \(1 \leq p \leq \infty\) at the univariate and multivariate levels. Furthermore, the multivariate cases of radial and non-radial approaches over the shell and ball are also presented and discussed. An application of the results obtained for \(\Psi (x) = e^x\) is included.
reviewed by: James A. Oguntuase
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 7455689
zbMATH Keywords: fractional calculus
zbMATH Keywords: fractional derivatives
zbMATH Keywords: integral inequalities
zbMATH Keywords: fractional Iyengar inequality
zbMATH Keywords: right and left \(\psi\)-Hilfer and Hilfer fractional derivatives
MaRDI profile type: Publication
full work available at URL: mfc.2021004
OpenAlex ID: W3150922274
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DOI: 10.3934/MFC.2021004
description: scientific article; zbMATH DE number 7455689