$\psi$-Caputo Fractional Iyengar's Type Inequalities

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, Erdélyi-Kober. The inequalities in this article are with respect to $L_p$ norms, $1\le p\le \infty .$ The tools used in the analysis are based on Taylor's formulae for $\psi$-Caputo fractional derivatives.