Some Riemann-Liouville fractional integral inequalities of corrected Euler-Maclaurin-type

Hezenci F., Budak H.

JOURNAL OF ANALYSIS, cilt.32, sa.3, ss.1309-1330, 2024 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 32 Sayı: 3
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s41478-024-00753-0
  • Dergi Adı: JOURNAL OF ANALYSIS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.1309-1330
  • Kocaeli Üniversitesi Adresli: Hayır

Özet

In this research article, an equality is established for Riemann-Liouville fractional integral. With the help of this equality, some corrected Euler-Maclaurin-type inequalities are established for the case of differentiable convex functions by using to the well-known Riemann-Liouville fractional integrals. Several important inequalities are obtained by taking advantage of the convexity, the Holder inequality, and the power mean inequality. Moreover, we give example using graph in order to show that our main results are correct. Furthermore, we provide our results by using special cases of obtained theorems.