$\pmb{\psi}$-Caputo Fractional Iyengar's Type Inequalities

TL;DR

This paper introduces new Iyengar type inequalities using $ ext{psi}$-Caputo fractional derivatives, generalizing known derivatives and establishing inequalities in $L_p$ norms through Taylor's formulae.

Contribution

It develops novel Iyengar inequalities based on $ ext{psi}$-Caputo fractional derivatives, extending existing fractional derivative frameworks.

Findings

Established inequalities in $L_p$ norms for $ ext{psi}$-Caputo derivatives.

Generalized classical fractional derivatives like Riemann-Liouville and Hadamard.

Utilized Taylor's formulae for fractional derivatives in the analysis.

Abstract

In this paper, we establish Iyengar type inequalities utilizing $\psi$-Caputo fractional derivatives that is, fractional derivative of a function with respect to another function, which is generalization of some known fractional derivatives such as Riemann-Liouville, Hadamard, Erd\'{e}lyi-Kober. The inequalities in this article are with respect to $L_{p}$ norms, $1\leq p \leq \infty.$ The tools used in the analysis are based on Taylor's formulae for $\psi$-Caputo fractional derivatives.