Taylor's formula and integral inequalities for conformable fractional derivatives

TL;DR

This paper develops Taylor's formula for conformable fractional derivatives and uses it to extend classical integral inequalities to conformable fractional calculus, broadening the mathematical tools available for fractional analysis.

Contribution

The paper introduces Taylor's formula for conformable fractional derivatives and extends several classical integral inequalities to this new setting.

Findings

Extended Steffensen, Chebychev, Hermite-Hadamard, Ostrowski, and Gruss inequalities to conformable fractional calculus.

Provided a new framework for applying Taylor's formula in fractional calculus.

Enhanced the mathematical understanding of inequalities in the context of conformable fractional derivatives.

Abstract

We derive Taylor's Formula for conformable fractional derivatives. This is then employed to extend some recent and classical integral inequalities to the conformable fractional calculus, including the inequalities of Steffensen, Chebychev, Hermite-Hadamard, Ostrowski, and Gruss.