NEW INTEGRAL INEQUALITIES FOR s-CONVEX FUNCTIONS OF THE SECOND SENSE VIA THE CAPUTO FRACTIONAL DERIVATIVE AND THE CAPUTO–FABRIZIO INTEGRAL OPERATOR

KEMALİ S., TINAZTEPE G., Işik İ. Y., Evcan S. S.

Rocky Mountain Journal of Mathematics, cilt.53, sa.4, ss.1177-1188, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 53 Sayı: 4
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1216/rmj.2023.53.1177
  • Dergi Adı: Rocky Mountain Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.1177-1188
  • Anahtar Kelimeler: Caputo fractional derivatives, Caputo–Fabrizio integral operator, convex functions, Hermite–Hadamard type inequality, s-convexity, specials means
  • Akdeniz Üniversitesi Adresli: Evet

Özet

Various integral inequalities for s-convex functions in the second sense are obtained by means of the Caputo fractional derivative and the Caputo–Fabrizio integral operator. Some generalizations of the Hermite–Hadamard type inequalities including the Caputo–Fabrizio integral operator are expressed for the functions whose derivatives are s-convex. Moreover, some inequalities involving these fractional operators are stated for the product of these functions. Inequalities involving special means and the digamma function are given as applications.