Enhanced bounds for Riemann-Liouville fractional integrals: Novel variations of Milne inequalities

Budak H., Hyder A.

AIMS MATHEMATICS, cilt.8, sa.12, ss.30760-30776, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 8 Sayı: 12
  • Basım Tarihi: 2023
  • Doi Numarası: 10.3934/math.20231572
  • Dergi Adı: AIMS MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.30760-30776
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

In this research article, we present novel extensions of Milne type inequalities to the realm of Riemann-Liouville fractional integrals. Our approach involves exploring significant functional classes, including convex functions, bounded functions, Lipschitzian functions and functions of bounded variation. To accomplish our objective, we begin by establishing a crucial identity for differentiable functions. Leveraging this identity, we subsequently derive new variations of fractional Milne inequalities.