New Conformable Fractional Operator and Some Related Inequalities

UÇAR D.

Filomat, cilt.35, sa.11, ss.3597-3606, 2021 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 35 Sayı: 11
  • Basım Tarihi: 2021
  • Doi Numarası: 10.2298/fil2111597u
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.3597-3606
  • Anahtar Kelimeler: Beta-integral, Hermite-Hadamard inequality, Steffensen inequality, Taylor’s formula
  • Uşak Üniversitesi Adresli: Evet

Özet

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.