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

Abstract

In this paper, we establish Iyengar type inequalities utilizing ψ-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 ≤ p ≤ ∞. The tools used in the analysis are based on Taylor's formulae for ψ-Caputo fractional derivatives.