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, vol.53, no.4, pp.1177-1188, 2023 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 53 Issue: 4
  • Publication Date: 2023
  • Doi Number: 10.1216/rmj.2023.53.1177
  • Journal Name: Rocky Mountain Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.1177-1188
  • Keywords: Caputo fractional derivatives, Caputo–Fabrizio integral operator, convex functions, Hermite–Hadamard type inequality, s-convexity, specials means
  • Akdeniz University Affiliated: Yes

Abstract

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.