Some new Boole’s inequalities with respect to the middle ending point using k-conformable fractional integral operators via different classes of differentiable functions

Benaissa B., Azzouz N., BUDAK H., Kashuri A.

Filomat, vol.40, no.2, pp.515-535, 2026 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 2
  • Publication Date: 2026
  • Doi Number: 10.2298/fil2602515b
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.515-535
  • Keywords: Boole inequality, Bounded function, h-Convex function, Hölder’s inequality, k-Comformable fractional operators, Lipschitzian functions, Middle ending point, Power-mean inequality
  • Kocaeli University Affiliated: No

Abstract

The objective of this study is to formulate a new definition of k-conformable fractional operators and to elucidate their boundedness and semigroup characteristics. Furthermore, we introduce an innovative identity for differentiable h-convex functions that employs k-conformable fractional operators. By employing this identity, we have formulated novel inequalities applicable to bounded functions as well as Lipschitzian functions. In the subsequent section, we utilized h-convexity in conjunction with the power-mean inequality and Hölder’s inequality, respectively.