Examining the Hermite–Hadamard Inequalities for k-Fractional Operators Using the Green Function

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YILDIZ Ç., Cotîrlă L.

Fractal and Fractional, cilt.7, sa.2, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 7 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.3390/fractalfract7020161
  • Dergi Adı: Fractal and Fractional
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus, INSPEC, Directory of Open Access Journals
  • Anahtar Kelimeler: Hermite-Hadamard inequality, convex functions, green functions, k-Riemann-Liouville fractional operators
  • Atatürk Üniversitesi Adresli: Evet

Özet

For k-Riemann–Liouville fractional integral operators, the Hermite–Hadamard inequality is already well-known in the literature. In this regard, this paper presents the Hermite–Hadamard inequalities for k-Riemann–Liouville fractional integral operators by using a novel method based on Green’s function. Additionally, applying these identities to the convex and monotone functions, new Hermite–Hadamard type inequalities are established. Furthermore, a different form of the Hermite–Hadamard inequality is also obtained by using this novel approach. In conclusion, we believe that the approach presented in this paper will inspire more research in this area.