New Conformable Fractional Operator and Some Related Inequalities

UÇAR D.

Filomat, vol.35, no.11, pp.3597-3606, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 11
  • Publication Date: 2021
  • Doi Number: 10.2298/fil2111597u
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.3597-3606
  • Keywords: Beta-integral, Hermite-Hadamard inequality, Steffensen inequality, Taylor’s formula
  • Uşak University Affiliated: Yes

Abstract

In this study, we introduce a new conformable derivative, namely the beta-conformable deriva-tive. We derive Taylor’s theorem for this derivative. We also investigate some new properties of Taylor’s theorem and some useful related theorems for the beta-conformable derivative. In the light of the new oper-ator, we extend some recent and classical integral inequalities including Steffensen and Hermite-Hadamard inequality.